Frequency of post-traumatic symptoms and stress disorders in combatants with BMD and TABR (%).
\\n\\n
More than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\\n\\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\\n\\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\\n\\nAdditionally, each book published by IntechOpen contains original content and research findings.
\\n\\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\\n\\n\\n\\n
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Simba Information has released its Open Access Book Publishing 2020 - 2024 report and has again identified IntechOpen as the world’s largest Open Access book publisher by title count.
\n\nSimba Information is a leading provider for market intelligence and forecasts in the media and publishing industry. The report, published every year, provides an overview and financial outlook for the global professional e-book publishing market.
\n\nIntechOpen, De Gruyter, and Frontiers are the largest OA book publishers by title count, with IntechOpen coming in at first place with 5,101 OA books published, a good 1,782 titles ahead of the nearest competitor.
\n\nSince the first Open Access Book Publishing report published in 2016, IntechOpen has held the top stop each year.
\n\n\n\nMore than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\n\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\n\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\n\nAdditionally, each book published by IntechOpen contains original content and research findings.
\n\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\n\n\n\n
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These metals are widely used in this kind of engineering because they have unique combinations of mechanical properties (strength, toughness, and ductility) as well as special physical characteristics (thermal and electrical conductivity), which cannot be achieved with other materials. In addition to thousands of traditional alloys, many exciting new materials are under development for modern engineering applications. Metallurgical engineering is an area concerned extracting minerals from raw materials and developing, producing, and using mineral materials. It is based on the principles of science and engineering, and can be divided into mining processes, which are concerned with the extraction of metals from their ores to make refined alloys, and physical metallurgy, which includes the fabrication, alloying, heat treatment, joining and welding, corrosion protection, and different testing methods of metals. Conventional metal forming/shaping techniques include casting and forging, which remains an important processing route. Electrodeposition is one of the most used methods for metal and metallic alloy film preparation in many technological processes. Alloy metal coatings offer a wider range of properties than those obtained by a single metal film and can be applied to improve the properties of the substrate/coating system. This book covers a wide range of topics related to recent advancements in metallurgical engineering and electrodeposition such as metallurgy forming, structure, microstructure properties, testing and characterizations, and electrodeposition techniques. 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Preservation of mental health and extension of professional longevity of combatants are the most urgent task of departmental psychiatry, as they are the most important element of public health, largely determining the economic and social well-being of the nation.
\nWhen considering the mental health of combatants in the context of the characteristics of the psychosocial environment and the dynamics of personal characteristics in the process of stress service, many authors note the presence of situational and dynamic subclinical changes that do not lead to social maladaptation in the usual conditions (in the circle of colleagues) [16], but significantly worsen the family sphere of functioning and contribute to a decrease in the quality of life.
\nIssues of psychological prevention of the formation of borderline mental disorders (BMD) and destructive and addictive behavior of combatants come to the fore in their social and psychological significance: suicidal and antisocial actions, use of drugs, and alcohol abuse [5].
\nThe structure of mental disorders in combatants in recent decades is characterized by a predominance of acute psychogenic pathological disorders with a significant reduction in the number of reactive psychosis. Over time, the structure of the social and medical consequences of wars for persons involved in extreme situation (ES) begins to prevail in the BMD, which lead not only to a decrease in the quality of life but also premature disability [6].
\nCombatants’ BMD are characterized by a wide range of mental illnesses from mild affective disorders and post-traumatic stress disorder (PTSD) to severe personality disorders.
\nThe Russian army began fighting in the North Caucasus region (NCR) against the separatists on December 11, 1994—it was the most massive and brutal war in the history of modern Russia. On August 31, 1996, the fight ended with the signing of the Khasavyurt agreement. However, the end of the conflict did not bring peace and tranquility. Kidnappings and murders of people, terrorist attacks on the territory of Russia led to the second stage of the military confrontation with the need to involve professional employees—members of law enforcement agencies. Fighting clashes took place in the territory of some republics—Chechnya, Ingushetia, Dagestan, and Kabardino-Balkaria. According to the general staff of the armed forces of the Russian Federation, during the period of hostilities in 1994–2009, the irretrievable losses of the Russian security agencies in the North Caucasus amounted to killed and dead of more than 8500, prisoners and missing of 510, and wounded of more than 70,000 people.
\nThe dynamics of personal changes in combatants indicates the deterioration of their mental health; there are emotional and behavioral stress, hyperactivity, a tendency to aggressive reactions, signs of social maladaptation, psychasthenic features, introversion, and emotional coldness, which contribute to the change of social functioning and social disintegration in the absence of clinically expressed psychopathology [14]. Therefore, it is necessary to detect these violations early and carry out medical and rehabilitation measures with subsequent monitoring of mental health of the participants of the fight.
\nAmong the clinical forms of BMD, to identify the combatants, the most common are an organic disorder with personality disorders, affective disorders and organic mental syndrome (F06, F07 according to ICD-10), somatoform disorders (F45), PTSD (F43.1), adjustment disorders (F43.2), and chronic changes of personality after the experience of catastrophe (F62.0).
\nCombatants’ BMD are significantly different from civilian neuroses on the specifics of the formation of the clinical symptoms and clinical manifestations; it is consistent with the formation of neurosis on the background of acquired and eventually increasing “accentuation of combatant” [17]. Earlier, the sudden onset of psychopathological symptoms was described against the background of external well-being, in acute conflict situations, often reflecting the internal feelings of a combatant [6].
\nFrom the point of view of S. Sukiasyan [14], BMD formed under the influence of combat mental trauma have similarities with neuroses in civilians. He distinguishes the following differences due to the etiopathogenesis of the disease and its dynamics: (a) the cause of the disease is characterized by an extreme occurrence, (b) the disorder occurs simultaneously from a large number of people, and (c) stress experienced by a person that is considered senseless leads to feelings of guilt for what happened with another person (death, injury, etc.).
\nAccording to M. Aksenov et al. [2], psychogenic neurotic states in persons of dangerous professions are presented by structured and relatively stable borderline disorders in their “classical” forms of manifestation (hysterical, dissociative, depressive, obsessive, anxiety-phobic, asthenic patterns, “neurosis of exhaustion”).
\nA distinctive feature of combatants’ BMD is the presence of an alcohol component, which is an integral part of the structure of mental disorders and before the formation of symptoms of dependence. In comorbid alcohol and drug disorders, there is no stage of formation of dependencies, in the structure of violations prevailing mainly psychopathic component. Drug dependence is more common among combatants who have had occasional drug use during fighting, who have not had sufficient socialization in peaceful life, and who had clinical signs of PTSD with a lack of timely treatment.
\nA special role among all combatants’ BMD is given to PTSD. Psychotraumatic events of combat nature can lead to the formation of chronic forms of PTSD, often occurring exclusively at the subclinical level, while disrupting the social functioning and quality of life in the participants of the fight. The following clinical variants of anxiety, explosive, dysphoric, depressive, somatoform, and conversion are described [4].
\nDescriptions of the clinical picture of PTSD include polymorphic asthenic, obsessive-phobic, and anxiety-depressive symptoms. According to J.Alexander [1], rare fully phenomenologically defined clinical variants of PTSD, there is a tendency to combination with the socio-stress disorders.
\nManifestations of post-traumatic stress disorder are often protracted, forming an average of 2–6 months after exposure to a traumatic situation. Personality disorders caused by battle mental trauma continue to be one of the most difficult areas of military psychiatry, both in clinical and diagnostic and in medical and expert aspects. Shortcomings in diagnostic approaches in the early stages lead to the identification of diseases at the stage of “deep implantation” of psychopathological symptoms in the personality, which later becomes the cause of the formation of pronounced personality disorders with subsequent disability of combatants.
\nIgnoring the symptoms of borderline mental disorders or their late detection, a formal approach by specialists in their diagnosis leads to the formation of chronic neurotic disorders, which significantly reduces the quality of life of combatants, increases the risk of manifestations of various forms of deviant behavior (antisocial, suicidal, addictive) [10].
\nTo explore the mental health of combatants involved in fighting in the North Caucasus, a continuous survey of 1537 men—employees of power structures of Russia returned from the trip after the execution of service and combat tasks in the special conditions as a member of integrated fighting units in the period 2006–2009—was carried out. Among all surveyed on the level of mental health identified after participating in the hostilities, believable: (a) Seven hundred twenty-five persons (45.7%)—healthy combatants, whom the therapy was not required, and rehabilitation assistance was not provided. (b) Four hundred ninety-seven people (31.3%)—persons who for 6 years prior to the survey according to the data of the outpatient cards were identified with short-term affective behavioral responses (TABR); during this survey of clinical data on the presence of formed BMD in this group which was not revealed, they were provided with psychocorrectional assistance by psychologists at the place of service. (c) Three hundred fifteen people (19.8%)—they were identified with adaptation disorders (RA) and PTSD; in this regard therapy and medical and psychological rehabilitation were carried out.
\nThree hundred eleven combatants were identified as having different TABR, which were recorded in the outpatient records of combatants by psychiatrists or neurologists during the 6-year period preceding our study (Group 1). These states occurred in the form of short-term emotional-maladaptive states and behavioral disorders and belonged to the pre-painful level (305 people). In Group 2 clinically formed BMD were revealed: AD was observed in 166 people (54.4%), among them are short-term depressive reaction (F 43.20)—35 (21.1%), prolonged depressive reaction (F 43.21)—31 (18.6%), mixed anxiety and depressive reaction (F 43.22)—35 (21.1%), violations of other emotions (F 43.23)—21 (12.6%), with prevalence of behavior disorders (F 43.24)—34 (20.5%), and mixed disorder of emotions and behavior (F 43.25)—10 (6.1%). Clinically designed PTSD was diagnosed in 139 people (45.6%) including anxiety type—36 (25.9%), explosive—33 (23.9%), somatoform—38 (27.6%), and conversion—31 (22.6%).
\nOur data confirm the studies of many authors who note the high prevalence of BMD among combatants around the world (especially in recent decades), which is associated with the extreme nature of service and participation in the settlement of ethnic conflicts [12, 17].
\nThe combatants from the AD had emotional disorders in the form of anxiety and depression, periodically arising dysphoria of different severities depending on the clinical variant of the AD. All combatants registered a violation of interpersonal communication with a pronounced irritability, hot temper, and distrust of others.
\nDreams of combat content in all combatants with PTSD presented painful scenes with a sense of threat to life (“could not defend”; “shot, but the bullets flew by”; “the corpses of the dead came to life”); dreams were accompanied by fear and vegetative symptoms (heartbeat, sweating). Depression, oppressive tension that is not a characteristic of earlier, increased sensitivity to everyday stimuli (loud sounds, the smell of gunpowder, gasoline), alertness, suspicion, and “over vigilance” were noted. There was a fear of open spaces with a sense of threat from the outside (squares, markets, and lawns were associated with “stretch marks,” fear of undermining, unfinished buildings with the threat of sniper fire, death, pits on construction sites with “graves,” and mass death of people).
\nClinical manifestations of PTSD differed depending on the course of the disease. In combatants with an alarming type of PTSD, the structure of the disease was dominated by the symptoms of the neurotic circle: unmotivated anxiety, frequent mood changes, sleep disorders (difficulty in falling asleep, early awakenings, lack of a sense of rest after a night’s sleep), lethargy, weakness, and “heaviness in the head.”
\nIn persons with an explosive type of PTSD, pronounced irritability and discontent were observed. They were characterized by resentment, vindictiveness, hostility to others, a tendency to solve everyday problems with the help of physical force, alertness, suspicion, vulnerability, and negativity. On the background of the overall tension, reducing the adaptive capacity of the neurotic tendency to impulsive reactions traced the difficulty in volitional control of negative emotions in everyday life; various forms of maladaptive behavior, such as excessive alcohol consumption and episodic use of psychoactive substances (PAS), were observed.
\nThe structure of somatoform-type PTSD was dominated by pain in the region of the heart, in the course of the gastrointestinal tract. There was a pronounced hypochondriac fixation on these symptoms and an alarming expectation of their amplification, which forced patients to contact general practitioners, at the same time, periodically stated functional cardio-pathologies, dizziness, neuralgia, sleep disorders, headaches, nausea, vomiting, urological manifestations, and sexual dysfunction.
\nIn combatants with a conversion type of PTSD in the clinic, the symptoms of increasing excitement with a lack of criticality to the disease prevailed, acute demonstrative reactions to external stimuli associated with the main traumatic factor, unmotivated initiative, increased chatter, inflated self-esteem, and the search for “perpetrators of the tragedy” with the desire for revenge. There were episodes of affective narrowing of consciousness with bouts of rage, physical aggression, and lack of guilt.
\nAnalysis of clinical symptoms in TABR and BMD combatants showed that PTSD symptoms, such as reliving traumatic events and nightmares, were observed in both groups of combatants but were significantly more frequent in Group 2. “Flashback” symptoms with pronounced psychosomatic manifestations in the form of tachycardia, sweating, and increased blood pressure with repeated trauma are recorded in both groups but most often in combatants with BMD. Hallucinations when falling asleep were only observed in individuals of Group 2. Dissociative manifestations to trigger the incentives in the structure of symptom re-experiencing the traumatic event are significantly more prevalent in individuals with the TABR in history.
\nPhobic reactions to trigger stimuli were found in groups with approximately the same frequency. Avoidance of thoughts, feelings, and people (everything that reminded about the injury) was revealed in both groups of respondents, but the frequency is significantly higher in persons with BMD (Table 1).
\nSymptoms | \nTABR | \nBMD | \nР | \n|||
---|---|---|---|---|---|---|
n = 311 | \n% | \nn = 305 | \n% | \n|||
At the moment of threat | \nAmnesia | \n0 | \n0 | \n1 | \n0,3 | \n0.345 | \n
Fear | \n0 | \n0 | \n1 | \n0.3 | \n0.456 | \n|
Disorganization of behavior | \n5 | \n1.6 | \n6 | \n1.9 | \n0.367 | \n|
Narrowing of consciousness | \n0 | \n0 | \n6 | \n1.9 | \n0.458 | \n|
Repeated experiences | \n“Flashback” symptoms | \n79 | \n25.4 | \n195 | \n63,9 | \n<0.001 | \n
Nightmares | \n58 | \n18.6 | \n136 | \n44,6 | \n<0.001 | \n|
Hallucinations when falling asleep | \n0 | \n0 | \n10 | \n3.3 | \n465 | \n|
Phobic reactions on the trigger incentives | \n3 | \n0.9 | \n4 | \n1.3 | \n0.478 | \n|
Dissociative symptoms on the trigger incentives | \n12 | \n3.9 | \n6 | \n1.9 | \n<0.05 | \n|
Avoidance | \nThoughts, feelings | \n11 | \n3.5 | \n38 | \n12.5 | \n< 0.05 | \n
Human action | \n69 | \n22.9 | \n143 | \n46.8 | \n<0.001 | \n|
Psychogenic fugue | \n12 | \n3.9 | \n4 | \n1.3 | \n< 0.05 | \n|
Reduced interest in previously Significant events | \n9 | \n2.9 | \n92 | \n30.2 | \n<0,001 | \n|
Sense of detachment, isolation | \n7 | \n2.3 | \n29 | \n9.5 | \n< 0.05 | \n|
The decrease in the level of Emotional response | \n34 | \n10.9 | \n89 | \n29.2 | \n<0.001 | \n|
The feeling of lack of perspective | \n0 | \n0 | \n12 | \n3.9 | \n0.478 | \n|
Excitations | \nSleep disturbance | \n89 | \n28.6 | \n198 | \n64.9 | \n< 0.05 | \n
Irritability | \n78 | \n25.1 | \n264 | \n86.5 | \n< 0.05 | \n|
Temper | \n96 | \n30.9 | \n214 | \n70.1 | \n<0.001 | \n|
Violations of concentration of Attention | \n32 | \n10.2 | \n139 | \n45.6 | \n<0.001 | \n|
Signs of social and labor maladjustment | \n9 | \n2.9 | \n45 | \n14.6 | \n<0.001 | \n
Frequency of post-traumatic symptoms and stress disorders in combatants with BMD and TABR (%).
Note: P is calculated using Pearson’s χ2, and intergroup differences were significant at p < 0.05.
It should be noted that combatants with TABR were significantly more likely to have psychogenic amnesia in the structure of the avoidance symptom than those with BDM.
\nSymptoms of emotional deficits with social introversion, such as a decrease in interest in previously significant events, a sense of detachment and isolation, and a decrease in the level of emotional response were found in both groups of respondents but were significantly more often present in people with BDM. A sense of lack of perspective was present in individuals with only clinically formed BDM (Table 1).
\nIn the combatant with TABR, clinical symptoms included maladaptive emotional and behavioral responses with symptoms characteristic of PTSD, but their duration and severity were significantly shorter and did not fit into the clinical criteria of the disease. In persons from the group with PPR, clinical symptoms were more pronounced, long-lasting, and polymorphic.
\nActive and timely diagnosis of adverse mental health conditions in combatants, rehabilitation, and therapeutic measures is an urgent task of the departmental health [15].
\nMany researchers noted the importance of developing new approaches to the treatment and rehabilitation of combatants with BMD. Inconsistency in psychodiagnostic approaches and terminology often leads to disagreements of specialists and is an obstacle to the modern provision of the necessary complex medical and psychological care.
\nRehabilitation is a complex of consistently held measures of medical, social, psychological, and pedagogical nature, aimed at the restoration of the individual to the level of her social activity.
\nAn important aspect of the success of BMD therapy is a personality-oriented approach that takes into account premorbid personality characteristics [7]. Combatants with harmonious traits, BMD treatment, and social readaptation are more successful in the near and in the remote period after participation in the war.
\nPsychotherapists identify the main directions of psychotherapy of combatants with combat mental trauma: restoration of a sense of value of life, control over their emotions, and restoration of destroyed social positive attitudes [12]. At the same time, the proposed techniques of work, long-term enough that in real conditions of service with existing employees is almost impossible to implement.
\nAt an early stage, as the practice of military conflicts in Afghanistan, the Persian Gulf, Vietnam, shows, it is advisable to carefully identify combatants who have received battle mental injuries and to maintain confidentiality, as the mechanism of “psychiatric stigma” is included. “Fatigue after a fight” in most cases is transformed into PTSD, which is a natural reaction of a person who finds himself in a war.
\nO. Yurkovsky fully described the stages and types of rehabilitation treatment of combatants with BMD, which include a set of medical, psychological, and social measures in inpatient and outpatient settings. The rehabilitation of patients with PTSD in the form of organization of the school, the basic principles of which are: balance, adaptability, and prevention; stages and continuity; complexity; and the concept of psychosocial rehabilitation of veterans of the war in Afghanistan, including three stages, is described: allocation of the main streams of combatants; conducting the main rehabilitation course (using special assistance centers); and supporting medical, psychological, and social methods [20].
\nDevelopment of the organization of necessary assistance to combatants should be based on a multi-professional, integrated approach with brigade methods and involvement of psychiatrists, psychotherapists, clinical psychologists, and drug addicts (in connection with the epidemic of drug use in the world and in Russia in particular). The most significant strategic miscalculation of the rehabilitation service creation is that the foundation on which the service is built is not defined [18].
\nMany experts in the field of mental health noted that the rehabilitation and therapy of veterans of combat operations are not sufficient; in this regard, they have the most pronounced risk of BMD and deviant behavior, which leads to a decrease in professional reliability and social functioning in general [11, 19].
\nS. Litvintsev notes that the treatment of persons with PTSD is advisable to produce in specialized departments and centers; the system of which in our country has not yet been established [9].
\nThe sequence and complexity of rehabilitation treatment are dictated by the need to resocialize combatants to reduce the negative psychosocial consequences in the modern society [7, 13].
\nWhen treating and rehabilitating combatants with PTSD, it is important to balance clinical and social approaches and motivate patients to recover quickly.
\nIn literature there are conflicting data on the evaluation of the effectiveness of therapy and rehabilitation of participants in hostilities. The analysis of the long-term results of rehabilitation measures conducted by O. Yurkovsky [20] showed that 88.5% of patients were successfully adapted and the effectiveness of treatment remained during the year. The effectiveness of therapy and rehabilitation depends on the timeliness of treatment, favorable premorbid, social support, and the absence of concomitant somatic diseases [8].
\nRehabilitation of persons with combat PTSD is a complex problem requiring improvement of organizational approaches and development of programs with the participation of various specialists involved in mental health.
\nThe use of psychopharmacotherapy in the treatment of BMD in combatants allows to stop psychopathological symptoms in the early stages, to increase the effectiveness of crisis psychotherapy, to reduce anxiety and aggression, to neutralize negative emotional reactions, and to improve interpersonal communication and social interaction.
\nThe choice of methods of medical treatment of BMD in combatants is based on clinical symptoms and is prescribed taking into account the main psychopathological syndromes and clinical forms in accordance with the standards of psychiatric care.
\nWith the predominance of depressive symptoms in the picture of BMD, it is advisable to use antidepressants (selective serotonin reuptake inhibitors and tricyclic antidepressants).
\nIn the case of the presence of PTSD and AD structure of alarming symptoms with sleep disorders, short course of explosive prescribe benzodiazepine tranquilizers and/or small neuroleptics.
\nIn conversion disorders, behavior correctors are mainly used. Antidepressants are not used due to the fact that they increase the dissociative symptoms.
\nIn the case of an explosive version of PTSD and AD, behavioral disorders are corrected with drugs with predominantly sedative effect; in some cases, a good effect is observed when taking lithium drugs due to stabilization of the emotional state.
\nIn the treatment of short-term depressive reactions caused by AD and PTSD with symptoms of anxiety and depression, selective serotonin reuptake inhibitors are most often used.
\nA good effect in the treatment of PPR, in the structure of which is dominated by anxiety and hypochondriac symptoms, as well as insomnia is noted when using benzodiazepine tranquilizers in the course 2–3 weeks, with gradual abolition.
\nIn combatants due to the negative impact of stresses of official activity after the execution of operational tasks in special conditions, often there are situational-due affective reactions, which are accompanied by anxiety and anxiety-phobic symptoms, which require the use of drugs with anxiolytic action. Their advantage is the absence of addiction and withdrawal syndrome, as well as a minimum number of side effects.
\nIn addition to drug therapy, combatants with BMD are provided with psychotherapy to respond to negative feelings and change attitudes to traumatic events. The main difficulty is the establishment of trusting contact, which is associated with the characteristics of patients that expressed distrust of the environment.
\nWhen conducting psychotherapy at the initial stage of medical rehabilitation, the presence of “combatant accentuation,” in the structure of which there is a formed distrust, unwillingness to seek help, skepticism, difficulties in interpersonal communication, and increased irritability and temper. These features often lead to conflicts with medical staff and psychologists. In combatants with PTSD, preference is given to individual forms of psychotherapy, especially at the stationary stage, since collective and group psychotherapy in the stage of acute clinical symptoms causes protest reactions in some people with BMD in the form of explosive outbreaks and dissociative symptoms.
\nThe establishment of empathic, trusting relationships between the patient and the psychotherapist is a critical therapeutic factor necessary for the effectiveness of therapy. When building communication in the process of psychotherapeutic treatment, it is necessary to take into account the personal characteristics of patients [3].
\nPsychotherapy with combatants is aimed at:
\nFormation of motivation for treatment and overcoming of the stigmatized attitude to the treatment process.
Combatant study of their psychological and personal characteristics.
Correction of response patterns in civilian life.
Formation of adaptive behavior skills in the service and at home.
Training in the techniques of psychical self-regulation and increase of their psychological capabilities for gaining control of emotional reactions.
At the initial stage of rehabilitation, it is advisable to conduct individual rational psychotherapy with all combatants—for the interpretation of the nature and causes of traumatic stress through logical re-persuasion, the formation of motivation for psychotherapeutic treatment, and overcoming the stigmatized attitude to psychotherapeutic assistance. The means of psychological influence are persuasion, explanation, and distraction. The main purpose of this psychotherapeutic method is to study the patient’s personality, evaluation, and correction of inadequate emotional and behavioral stereotypes of the patient, which determine the violation of his psychological and social functioning.
\nThe use of art therapy contributes to the additional diagnosis of personal problems, affective disorders, further de-actualization of traumatic events, the expansion of adaptive reserves, self-esteem, and mood correction. The plot should be connected with the peculiarities of the combatants’ attitude, feelings, and experiences reflecting the stressful effects. The therapy is conducted individually and effective combatants as with adjustment disorder, and PTSD. Painting and drawing techniques are used with various materials (gouache, pencil, oil, watercolor, artistic coal). Depending on the material chosen by the combatant, the duration of the session is from 30 minutes to 1.5 hours, and the number of sessions per course of therapy is from 3 to 10 times.
\nAs an example, illustrating the theoretical material, we present the work of two combatants diagnosed with PTSD. A work of art is made with charcoal.
\nIn the examination of combatant K, 27 years old, after returning from the NCR, he was found to have pronounced explosive and dysphoric symptoms, the violation of communicative processes, social isolation, pessimism, and a diagnosis of PTSD, dysphoric type (a plot—“a lone rider,” Figure 1A).
\n(A) Combatant K—Before treatment. Diagnosis: PTSD, dysphoric type. (B) Combatant K—In a month of therapy.
After the medical and psychological rehabilitation, improvement of the emotional background and reduction of the main psychopathological manifestations were noted (a plot —“nest,” Figure 1B).
\nDuring the examination of combatant M. after returning from the NCR (a plot—“warrior,” Figure 2A), there was a pronounced aggressive-dysphoric mood, violation of interpersonal communication skills, negativity, and “defensive position.” After the medical and psychological rehabilitation, the stability of the emotional background, balance, and reducing anxiety and aggression were noted (a plot—“sea, calm,” Figure 2B).
\n(A) Combatant M—Before treatment. Diagnosis: PTSD. (B) Combatant M—in a month of therapy.
In the works of the combatant K, 27 years old, diagnosed with PTSD, an alarming type, there was also a positive dynamics of mental state. A work of art is made with charcoal. After returning from the NCR (a plot—“a wolf howls at the moon”), expressed anxiety and depression symptoms, a violation of communication processes, social isolation, and pessimism were noted (Figure 3A). After the medical and psychological rehabilitation (a plot—“winter landscape”), the stability of the emotional background, balance, and lack of anxiety and depression on the background of introversion were noted (Figure 3B).
\n(A) Combatant K—Before treatment. Diagnosis: PTSD. (B) Combatant K—in a month of therapy.
The leading method in working with combatants is family psychotherapy, aimed at restoring family values and interpersonal relations in the family. The attention of the immediate environment is focused on the need to provide psychological assistance and family support to the combatants; it is explained that the return to peaceful life may be accompanied by difficulties. Family members are given a description of the combatant’s behavior, the problems that have arisen after combat stress are reported to be of a nonpermanent nature, and the family can help to deal with them.
\nOur data in the study of mental morbidity among combatants significantly differ from the studies of O. Shevtsova and V. Kokhanova, who revealed that the background of the increase in the number of BMD, dismissal among the military who underwent BND, is 61.4% due to clinical resistance to therapy and the presence of psychosocial consequences [19]. Similar data are noted in the works of D. Svechnikov and co-authors, who show that neurotic disorders in military personnel are the leading pathology for defense agencies, leading to early dismissal and extremely negative impact on the combat effectiveness of the army [11].
\nAccording to our data, the timely provision of professional assistance to combatants with the BMD not only does not lead to dismissal but also is not an obstacle to professional growth. In the process of rehabilitation of combatants with BMD, there is a positive trend: a month after the start of therapy in persons with RA is 83.3% and PTSD in 67.4% of cases; during the year 93.1 and 89.9% and in 4 years 98.9 and 96.6%, respectively. V. Shamrey noted that the identified violations in the combatants rarely led to a serious violation of social adaptation but felt sick as hindering the possibility of adequate realization of their personal potential; they did not associate them with the disease, regarded them as “growing up” [17].
\nThus, early detection of BMD and pre-pain conditions in combatants with appropriate poly-professional therapy leads to positive results, contributing not only to the preservation of mental health but also to further career growth.
\nFrom the viewpoint of mathematical systems, the time series observed in physics are usually regarded as coming from the Lagrangian systems, also called the conventional systems. The systems can be analyzed by the conventional Euclidean geometry [1]. However, the systems in practice are usually nonlinear and complex. Thus, a lot of interesting time series in nature are complex due to nonlinear phenomena derived from nonlinear dynamical systems [2]. The nonlinear dynamical systems have been described by Hamiltonian systems and dealt with by using symplectic geometry [3]. Symplectic geometry is an even dimensional geometry living on even dimensional spaces. Different from the conventional Euclidean geometry that measures 1-dimensional lengths and angles, the symplectic geometry studies the metric properties (such as area) and can preserve the system structure in the phase space [4]. Apart from applications on the classical dynamical systems to solve the equation problems, symplectic geometry has been also used on the studies of nonlinear time series [5, 6, 7, 8].
According to Takens’ embedding theorem, a time series can be reconstructed into an attractor in phase space [9]. The reconstructed attractor is a geometrical object that can reflect the underlying dynamical system. In order to better understand the nature of the underlying system, the attractor and its properties are characterized in the phase space by various mathematical methods, such as dimension, fractal geometry, Lyapunov exponent, entropy and symplectic geometry [1, 5, 10, 11]. For dimension, fractal geometry, Lyapunov exponent, entropy, there are a more extensive discussion with mathematical details in some research literatures [12, 13, 14, 15]. Here, we only introduce how to apply symplectic geometry theory to extract the information from the reconstructed attractor and its application on physics, engineering and biomedical engineering.
The reconstruction from a time series of observation is the first and most crucial step in nonlinear time series analysis. It is also the basis of applications of symplectic geometry on time series analysis. Takens’ embedding theorem allows us to reconstruct an equivalent attractor of the underlying dynamical system by embedding one time series. The theorem proves that the reconstructed attractor has the same dynamical characteristics as the attractor of the original system if the embedding dimension m is sufficiently large. Let a time series of observation x1, x2, …, xn. n is the number of samples. The reconstructed attractor can be given in N-dimensional space RN by the time-delay embedding [5]:
where the number of dots in the attractor is m = n-N + 1, the embedding dimension is N. X is also called as the trajectory matrix of the original system in phase space. The corresponding program is given by matlab software as follows:
----------------------------------
function matrixSignal = signalMatrix(x, N)
% ------Construct data matrix------
%
% Synopsis:
% matrixSignal = signalMatrix(x, N)
%
% Description:
% It constructs a data matrix from a time series as a column vector, i.e., a
% reconstruction attractor.
%
% Input:
% x a time series with the length n.
% N [1x1] Output dimension; N > 1 (default N = dim);
%
% Ouputs:
% matrixSignal [N x M] a data matrix (M = n-N + 1).
%
if nargin <2, N = 2; end
n = length(x);
M = n-N + 1;
matrixSignal = zeros(N,M);
for i = 1:N
matrixSignal(i,:) = x(i:M + i-1);
end
-------------------------------------
In the symplectic spaces, Hamiltonian system is the analysis fundamental for the real physical processes [4, 5]. A real system should be first described by a suitable Hamiltonian system, i.e. an even dimensional matrix. For a time series, its Hamiltonian matrix H can be defined by using its reconstructed attractor X.
Definition 2.1 Let X be a d-dimensional matrix in a real number field Rd. The matrix
Here, A is a d × d real number matrix.
Definition 2.2 For a d × d matrix A, the Hamiltonian matrix H can be defined:
Here, H is a 2d × 2d matrix.
Symplectic geometry focuses on the study of area measure in symplectic space R2n. Its basic concepts and basic properties are related but different from those of a Euclidean geometry (see Table 1).
Geometry space | Symplectic space | Euclidean space |
---|---|---|
Space dimension | 2n-dimension | n-dimension |
Unit matrix | unit symplect matrix: | unit matrix: |
Determinant of unit matrix | |J2n| = 1 | |In| = 1 |
Product calculation | symplectic inner product <x, y> | Inner product (x, y) |
Calculation measure | area | length |
Orthogonality | ||
Space basis | Adjoint symplectic orthonormal basis Q = {x1,x2, …, xm, y1, y2, …, ym}, m ≤ n; when determinant |Q| = 1, the basis Q is normal. | Orthogonal basis W = {x1,x2, …, xm}, m ≤ n; when |W| = 1, the basis W is normal. |
Orthogonal matrix | Symplectic matrix S | Orthogonal matrix W |
Analysis matrix | Hamiltonian matrix H HT = JHJ. | Symmetry matrix A AT = A = IAI. |
Matrix transformation | Hamiltonian transformation | Symmetry transformation |
Eigenvalues of the matrix | The eigenvalues of H are ±μ. | The eigenvalues μ of A are real. |
Eigenvectors of the matrix | The eigenvectors of H are symplectic orthogonal. | The eigenvectors of A are orthogonal. |
The comparison between symplectic geometry and Euclidean geometry.
In Euclidean space, the inner product is denoted as the measure of the length. The unit matrix is I, i.e. the main diagonal elements are 1, and the other elements are 0. Corresponding to the unit matrix I in Euclidean space, the unit matrix in symplectic space is defined as the unit symplectic matrix J, an even dimensional matrix:
The properties of the matrix J have:
Definition 2.3 For any two n-dimensional vectors x2n × 1 and y2n × 1, the normal symplectic inner product is defined by using the inner product of Euclidean space:
The normal symplectic inner product is also denoted briefly as the symplectic inner product in a real vector space R2n. When n = 1, there is:
The symplectic inner product is a bilinear antisymmetric nonsingular cross product. In symplectic space, the length of any vectors is equal to 0. But there exists the concept of symplectic orthogonal cross-course.
Definition 2.4 Let x and y be a 2n-dimensional real vector. If their symplectic inner product is equal to zero, i.e.:
then x and y are symplectic orthogonal. Otherwise, they are called as symplectic adjoint.
Definition 2.5 If a vector set {x1,x2, …, xm, y1, y2, …, ym} in the real symplectic space R2n (m ≤ n)is an adjoint symplectic orthonormal vector set, then the vectors xi and yi (i = 1, …,m, xi∈ R2n, yi∈ R2n) satisfy
where i, j = 1, 2, …, m. It is called as an adjoint symplectic orthonormal basis in the 2n-dimensional symplectic space. If aii = 1, the vector set {x1,x2, …, xm, y1, y2, …, ym} is a normal adjoint symplectic orthonormal vector set (a normal adjoint symplectic orthonormal basis in the space R2n).
The orthogonal of the Euclidean space is different from the symplectic orthogonal. If vectors x and y in the space Rn are orthonormal, then they satisfy:
where x ≠ y.
If a vector set {x1,x2, …, xm}∈Rn is an orthonormal vector set, then any two vectors in the set satisfy:
where i, j = 1, 2, …, m, i ≠ j. Eq. (17) is similar to Eqs. (14) and (15). In the n-dimensional Euclidean space, the set {xi} is denoted as an orthonormal basis. \tIf ||xi || = 1, the orthonormal basis is a normal orthonormal basis.
Theorem 2.1 Let {αi} be a normal adjoint symplectic orthonormal basis in a 2n-dimensional symplectic space Φ. Let the coordinates of any vectors β and γ in Φ be {x1, x2, … xn, xn + 1, …, x2n}T and {y1, y2, … yn, yn + 1, …, y2n}T, respectively. Referring to the basis {αi}, the coordinates can be described as:
where i = 1, 2, …, n. Then the symplectic inner product of β and γ is as follows:
Thus, the symplectic inner product operation is transformed to the matrix operation of ordinary vectors or matrices by applying a normal adjoint symplectic orthonormal basis.
Definition 2.6 Let S is a 2n × 2n matrix, if S satisfies:
then S is a symplectic matrix and the determinant |S| = 1 or − 1. Meanwhile, the inverse matrix and the transpose matrix of a symplectic matrix are a symplectic matrix, respectively. The symplectic matrix S is similar to an orthogonal matrix W in Euclidean space, like Eq. (20):
Theorem 2.2 The product of sympletcic matrixes is also a symplectic matrix.
Proof:
Let Si (i = 1, 2, …, n) be a symplectic matrix. The product matrix M:
According to the above definition of symplectic matrix, there are:
Thus, the product of symplectic matrixes is also a symplectic matrix.
Definition 2.7 If a 2n × 2n matrix H is a Hamiltonian matrix, then the matrix H satisfies the following properties:
where x and y are 2n-dimensional vectors. In other words, if an even-dimensional matrix H satisfies these properties above, the matrix H is a Hamiltonian matrix. In Euclidean space, a symmetric matrix A is similar to a Hamilitonian matrix H, like Eqs. (26) and (27):
Theorem 2.3 Let a matrix A be a n × n real number matrix, if it can be built into a 2n × 2n matrix H in symplectic space in the following pattern:
Then the matrix H is a Hamilton matrix.
Proof:
Let
where J is the 2n × 2n unit symplectic matrix. In terms of Definition 2.7, the matrix H is a 2n × 2n Hamiltonian matrix.
Theorem 2.4 Let a 2n × 2n matrix H be a Hamiltonian matrix. Then its properties keep unchanged at symplectic similar transform. That is, a Hamiltonian matrix H through a series of symplectic similar transforms is still a Hamiltonian matrix.
Proof:
According to Definition 2.6, let the matrix S be a symplectic transform matrix. Then, the inverse matrix S−1 is also a symplectic matrix. For a Hamiltonian matrix H, let SHS−1 be the matrix M under the symplectic similar transformation of the matrices S and S−1. Thus,
Therefore, M is also a Hamiltonian matrix. Moreover, the matrix M is similar to the matrix H. Therefore, the Hamiltonian matrix H can keep unchanged at symplectic similar transform in symplectic space.
The eigenvalues of a Hamiltonian matrix have the specific characteristics of the Hamiltonian matrix. However, the eigenvalues may be complex or repeated eigenvalues. In order to obtain the real eigenvalues of a Hamiltonian matrix H, symplectic QR decomposition method is applied to deal with the Hamiltonian H:
Let a 2n × 2n matrix H be (ATG; F –A), then
Build a 2n × 2n symplectic matrix Q and satisfy:
Here B is an upper Hessenberg matrix. Besides, the matrix Q can be a 2n × 2n Householder matrix.
Use the symplectic QR decomposition method to obtain eigenvalues:
The eigenvalues of the Hamiltonian matrix H with multiplicity n are
In symplectic space, the symplectic QR decomposition method allows the primary 2n-dimensional space transform into n dimensional space to resolve the eigenvalues of the Hamiltonian H, where the matrix Q is a symplectic unitary matrix. Thus, the consuming time of the calculation is only one fourth the number of floating-point operations. In general, one makes use of a Householder matrix instead of the matrix Q.
Theorem 2.5 If a 2n × 2n matrix Q is a Householder matrix, then the matrix Q is a symplectic unitary matrix.
Proof:
Let a Householder matrix Q
where, ‘*’ means the conjugate transposition. Then, there is
Therefore, the Householder matrix Q is a symplectic unitary matrix.
In symplectic space, the reconstructed attractor can keep its properties unchanged [5, 6]. Its symplectic geometry spectrums can be given by the symplectic geometry theory above. On the basis of Section 2.1 and 2.2, one can build a Hamiltonian matrix M from a time series of the observation. Due to the structure characteristics of the matrix M, its eigenvalues can be calculated by the 2n-dimensional symplectic space reducing into n-dimensional space. In terms of Theorem 1.5, a 2n × 2n symplectic Householder matrix Q can be constructed. The matrix P in the matrix Q can be calculated by the matrix A in the matrix M. The specific steps are as follows:
Let A be
If the vector
then, there is:
where E(1) = (1, 0, …, 0)T is a n × 1 unit column vector.
Then, the elementary reflective matrix P(1) can be calculated:
So, there is
Continue to deal with A(2) by repeating the above steps, let S(2) be
Then,
where E(2) = (0, 1, 0, …, 0)T is a n × 1 unit column vector.
Then, the elementary reflective matrix P(2) can be calculated:
Thus, we can get A(3) with all zeros elements except the first and second non-zero elements:
Repeat the same steps until A(n) becomes an upper triangle matrix, one can construct a Householder matrix P as follows:
Thus, a symplectic Householder matrix Q can be built to make the Hamiltonian matrix M transform as an upper Hessenberg matrix, namely:
where μ means the eigenvalue. The matlab program is as follow:
-------------------------------------
function [P, R] = householder (A)
% ------Solve Householder Transform Matrix------
%
% Synopsis:
% [P, R] = householder (A)
%
% Description:
% It solves a Householder matrix from a data matrix, i.e., a
% reconstruction attractor.
%
% Input:
% A [mRow x mCol] a data matrix.
%
% Ouputs:
% P [mRow x mRow] a Householder matrix
% R [mRow x mCol] an upper triangle matrix
[mRow, mCol] = size(A);
if mRow>mCol
A = A’;
[mRow, mCol] = size(A);
end
I_matrix = eye(mRow);
m = min([mRow, mCol]);
p = I_matrix;
for i = 1:m.
S = A(:,i);
if i > 1.
S(1:i-1) = 0;
end
alpha = sqrt(S’*S);
delta1 = S-alpha*I_matrix(:,i);
delta = sqrt(delta1\'*delta1);
if delta==0
delta = eps;
end
omega = delta1/delta;
p = I_matrix-2*omega*omega\';
A = p*A;
P = p*P;
end
R = A;
return
-------------------------------------
For the attractor matrix X of a time series, its symplectic geometry spectrums SGS are calculated by the eigenvalues of the A in descending order, that is:
where i = 1, …, n. n is the dimension of the attractor X.
To estimate the embedding dimension is usually the first step of nonlinear analysis [5]. For a time series, it is important to resolve a suitable embedding dimension of the observed system. Due to the measure-preserving charactistic of symplectic geometry, symplectic geometry spectrums can be used to estimate the embedding dimension of the system from a time series. With the increase of the dimension n in Eq. (61), the change of the symplectic geometry spectrums SGS in Eq. (60) tends to be flat at i = d (i∈(1,n))and enters the noise floor area, SGS1 > SGS2 > … > SGSd> > SGSd + 1 ≥ … ≥ SGSn,. That is, the eigenvalues exist σ1 > σ2 > … > σd> > σd + 1 ≥ … ≥ σn, then d is defined as the embedding dimension of the time series for the reconstruction system.
Symplectic entropy(SymEn) is a kind of entropy measure for a dynamic system in symplectic space [16]. Based on the symplectic geometry spectrums, the SymEn measures the energy distribution in symplectic space of a dynamic system from a time series. The distribution of the energy of the system is described by the eigenvalues σ in the relevant symplectic orthonormal bases of the symplectic space. In each base direction, the probability of the energy distribution can be given as follows:
where i denotes the ith base direction in the symplectic space,
Then,
The matlab program is as follows:
----------------------------------
function SymEn = SymplecticEntropy(A)
[Q, R] = householder(A);
delta = diag(R);
sum_delta = sum(delta);
p = delta./sum_delta;
SymEn = −sum(p.*log(p));
Return
-------------------------------------
The SymEn value represents the uncertainty of the entropy about the underlying probability distribution of a dynamic system in symplectic space, called Symplectic Entropy.
Symplectic principal component analysis (SPCA) is a kind of principal component analysis (PCA) to map the dynamic system from a time series into the symplectic space [17]. Due to the preserving-measure nature of symplectic geometry, symplectic principal components elucidate the dominant features of a time series for an underlying system. The principal components corresponding to larger eigenvalues capture the key relationship between the variables in symplectic space. The components corresponding to smaller eigenvalues are regarded to relate primarily to the less important components or noise in the time series. The analysis of eigenvalues are also called as the symplectic geometry spectrums analysis (SGSA) [6, 18, 19]. The corresponding components are also regarded as symplectic geometry mode decomposition (SGMD) [7, 8, 20, 21]. According to the symplectic geometry spectrums above, if the number of the chosen symplectic principal components is k, the corresponding principal eigenvector matrix p can be constructed by using the first k eigenvectors of the matrix P in the matrix Q. The corresponding principal eigenvalues are the first k eigenvalues in the symplectic geometry spectrum. If k = n, p = P. Otherwise, p ⊂ P. Then the reestimated attractor matrix
The corresponding pith principal component matrix
Then, the reestimated attractor matrix is equal to the sum of
The reestimated time series xr is equal to the sum of each principal component, i.e. the sum of projections in different directions. If i = 1, the reestimated time series is a reduced noise data based on the first principal component.
Symplectic geometry theory has been applied to deal with a time series in fields of physics, engineering, biomedical engineering [6, 7, 8, 11, 16, 17, 18, 19, 20, 21, 22, 23, 24], since Lei et al.(2002) first proposed a symplectic geometry method to estimate the appropriate embedding dimension from a time series [5]. Here, we will introduce four research cases in terms of the above theorem and properties of symplectic geometry for the time series analysis.
Case 1: Embedding dimension estimation for Lorenz chaotic time series [5].
Lorenz chaotic system was accidentally discovered by Edward Norton Lorenz [25], an American meteorologist, in 1963 when he was studying weather forecast, and was known as the first chaotic attractor. Since then, people began to study chaos, a random-like phenomenon. Lorenz chaotic time series x comes from Lorenz chaotic system, which is a three-dimensional dynamical system as follows [5]:
where σ = 10, b = 8/3, γ = 28. The state variable x is chosen as the analyzed data. The sampling interval is 0.005. The length n is 1000 points.
The attractor reconstructed from Lorenz chaotic time series x can reflect the Lorenz system. Here, the dimension of the reconstructed attractor is estimated by the above symplectic geometry method. Let the embedding dimension d be 3: 5: 23, where i = 1: d. The matlab program is as follows:
-------------------------------------
% Compute a Lorenz chaotic time series
% Example:
% state = [5 5 5];
% Ts = 0.005;
% N = 10000;
% y = calculate_lorenz(state, Ts, N);
% x = y(:,1);
function y = calculate_lorenz(state, Ts, N).
if nargin <1
state = [5 5 5];
Ts = 0.005;
N = 10000;
end
if nargin == 1
Ts = 0.005;
N = 10000;
end
if nargin == 2
N = 10000;
end
% set time span with specific times for the solution
T = 0:Ts:N*Ts;
% set a scalar relative error tolerance \'RelTol\' (1e-3 by default).
% and a vector of absolute error tolerances \'AbsTol\' (all components 1e-6% by default).
options = odeset(\'RelTol\',1e-4,\'AbsTol\',[1e-4 1e-4 1e-5]);
% solve Lorenz chaotic system
[t,y] = ode45(\'lorenzeq1\',T,state,options);
return
function ydot = lorenzeq(t,y)
% Lorenz equation
b = 8/3;
r = 28;
delta = 10;
A = [−delta delta 0;r − 1 -y(1);y(2) 0 -b];
ydot = A*y;
return
--------------------------------------
% Calculate the embedding dimension.
state = [5 5 5];
Ts = 0.005;
N = 10000;
y = calculate_lorenz(state, Ts, N);
x = y(:,1);
figure.
for N = 3:5:23
X = signalMatrix(x,N);
A = X*X’;
[Q, R] = householder(A);
delta = diag(R);
sum_delta = sum(delta);
d = log10(delta./sum_delta);
n = length(d);
plot(1:n, d, \'b*-\')
hold on
end
ylabel(\'log10(\\delta_{\\iti}/tr(\\delta_{\\iti}))\')
xlabel(\'{\\itd} = 3:5:23\')
axis([0 25–15 0])
-----------------------------------
Figure 1a shows the symplectic geometry spectrums SGS of x without noise according to the above equations based on symplectic geometry theory. We can see that the symplectic geometry spectrums turn abruptly into a flat area from i = 6, i.e. σ1 > σ2 > … > σ5> > σ5 + 1 ≥ … ≥ σd. So, the embedding dimension of the time series x can be estimated at 6. But from the Figure 1b, we can see that it is difficult for the SVD method to determinate the embedding dimension from the time series x. The results indicate that the symplectic geometry method could better determinate the embedding dimension from a time series due to its preserving-measure properties.
The embedding dimension estimation of Lorenz chaos series with no noise based on: (a) the symplectic geometry method; (b) the SVD method.
Case 2: Embedding dimension estimation for the surface EMG signal [5].
In the practical engineering research, a lot of time series data due to their complexity are considered to be nonlinear, such as the surface EMG signal in biomedical engineering. As a kind of non-invasive measure for the contracting skeletal muscles, the surface EMG signal reflects some information about the muscle, limb movements and loading of the bones and joints. It has been widely applied to assess biomechanical and motor control deficits and other functional disorders, as well as to diagnose neuromuscular problems. However, due to noise interference, the study of surface EMG signal is still a great challenge in biomedical engineering. Many researches indicate that the surface EMG signal is complex and nonlinear. The embedding dimension estimation of the surface EMG signal is usually critical to analyze its nonlinear features. As an example, we use the above symplectic geometry method to estimate the embedding dimension of the surface EMG signal during forearm supination. The length of the surface EMG signal is 1000 points. The data sampling frequency is 1 kHz. Figure 2a shows the raw surface EMG signal. Figure 2b gives the symplectic geometry spectrums SGS of the data in Figure 2a. From Figure 2b, the symplectic geometry spectrums SGS change slowly at d = 6 and turn into noise floor with the increase of the index i. Then, the embedding dimension can be estimated at 6 for the surface EMG signal during forearm supination.
The embedding dimension analysis of the surface EMG signal based on the symplectic geometry spectrums: (a) Typical surface EMG signal during forearm supination; (b) The symplectic geometry spectrums of the surface EMG data in (a), where abscissa is the analysis dimension d = 3, 8, 13, 18, 23, ordinate is \tSGSi = logσi/trσi, where the index i = 1: d.
Case 3: SymEn analysis of vibration signals on rolling bearings [11].
In the rotating machinery systems, it is extremely important for rolling bearings to detect faults from vibration signals. The Case Western Reserve University (CWRU) Bearing Data Center provides a website database for the vibration signals of bearings (
Symplectic geometry preserves the nature of a dynamic system under symplectic similar transformations. As an entropy measure in symplectic geometry, the SymEn value of a time series measures the lack of information in a dynamic system to reflect its properties. For the complexity of a rolling bearing, the SymEn estimate is applied to test its nonlinear characteristics from the vibration signals. Figure 2 shows the SymEn values of the vibration signals at the drive end and their surrogate data sets based on the null hypothesis of a Gaussian linear stochastic process. Here, the length of each data is 6000 points. The embedding dimension d = 7.
Meanwhile, the 39 sets of surrogate data are generated by the iterated amplitude adjusted Fourier transform (IAAFT) algorithm in the 95% confidence level [26]. From Figure 3, we can see that there are the significant differences between these SymEn values of the vibration signals of a rolling bearing and their surrogate data sets. The results indicate that the vibration data could contain nonlinear characteristics. The original vibration signals are not from a Gaussian linear stochastic process in the 95% confidence level but from a nonlinear dynamical system. It conforms that the rolling bearing system is a complex nonlinear dynamical system.
The nonlinear analysis of vibration signals based on the SymEn method: (a) for the normal condition (NC); (b) for the outer race fault (ORF); (c) for the rolling element fault (REF); (d) for the inner race fault (IRF). The abscissa is the SymEn values of vibration signals and their surrogate data.
Due to the complexity of rolling bearings, it is often thought that the high dimensional features can better identify the faults of rolling bearings [27, 28, 29]. However, the SymEn method can availably extract the low-dimensional features to identify the faults of rolling bearings from vibration signals quite precisely. Figure 4 shows the four working states of rolling bearings, i.e., NC, ORF, REF, and IRF, based on 2-dimensional features. The abscissa is the SymEn estimates of vibration signals at the drive end. The ordinate is those estimates of vibration signals at the fan end. We can see that the four states are obviously different. There are 100% accuracies by RBF classifier for the four states of the rolling bearings. Figure 5 plots the histogram of error values between output classes and target classes for the SymEn estimates as features of vibration signals.
The states analysis of rolling for bearings with the SymEn estimates.
The analysis of error values identification accuracies of four states.
Case 4: Noise reduction analysis of vibration signals based on SPCA [17, 30].
In the practical engineering measurement, the vibration data of rolling bearings have often become contaminated with noise. The noise reduction is also beneficial to analyze the measured data. The SPCA method preserves the intrinsic nonlinear nature of the raw data. The symplectic principal components can better retrieve dominant patterns from the noisy data. For the vibration signals of rolling bearings, the first symplectic principal component is used two times continuously to reduce the noise in the data.
The specific analysis procedures are as follows:
Build a Hamiltonian matrix from the measured data in terms of Eq. (1), Definition 2.1, 2.2 and Theorem 2.3;
Use the Eq. (44)–(59) to compute a symplectic Householder transform matrix Q for the symplectic QR decomposition in the SPCA method;
Construct the first symplectic principal component eigenvector matrix p1;
Calculate the first symplectic principal component coefficients S1, i.e.:
Get the first denoised data x1 from the reestimated matrix in the following:
Let the first denoised data x1 into the first step, and repeat the above steps, then obtain the second denoised data x3.
Figure 6 shows the effect of denoising for the vibration signals of rolling element fault (REF), No.225 data in the CWRU database [11]. For the rolling element fault at the drive end, the fault state can be seen clearly by the second reducing noise (see Figure 6a). For the vibration signals at the fan end without faults, the periodical characteristics in the normal state can be shown after the two reducing noise (see Figure 6b).
The two times denoising analysis for the vibration signals of rolling element fault (REF) in No.225 data from the CWRU database. (a) The abscissa is the number of data points; (b) the ordinate is the amplitude (v) of the data.
Moreover, the noise reduction method based on the symplectic geometry has been used to denoise several time series data of Lorenz chaotic system, duffing chaotic system, Chua’s chaotic system with noise, as well as the sunspot number [30]. The details can be found in literatures [17, 30].
Besides, the symplectic geometry method also further integrate other approaches to better investigate the fault extraction and identification for rotating systems, such as symplectic geometry mode decomposition [19] with power spectral entropy [7] as well as Lagrange multiplier [20], symplectic transformation based variational Bayesian learning [21].
This chapter introduces the symplectic geometry theory in the research field of the time series analysis in view of the complexity of a time series. Corresponding to Euclidean geometry, the basic concepts and basic elements of mathematics of the symplectic geometry are given, such as the symplectic space, symplectic transformation, Hamiltonian matrix, symplectic entropy (SymEn), symplectic principal component analysis (SPCA), and so on. Based on the symplectic geometry theory, the symplectic geometry spectrum analysis (SGSA), the symplectic entropy (SymEn) method and the symplectic geometry mode decomposition (SGMD) method are demonstrated to investigate the principal characteristics of a time series in the symplectic space. Meanwhile, the corresponding matlab programs are given. At last, in order to facilitate readers to learn, use and develop the symplectic geometry method, some applications of symplectic geometry on time series analysis are presented, such as the embedding dimension estimation, nonlinear testing, fault diagnosis, as well as noise reduction.
The embedding dimension estimation is often the first step in nonlinear time series analysis. Case 1 and 2 show the embedding dimension estimation of Lorenz chaotic time series and the surface EMG signal based on symplectic geometry spectrum. Moreover, the symplectic entropy method is applied to detect the nonlinearity of vibration signals on rolling bearings and identify the faults of vibration signals on rolling bearings (see Case 3). Considering the noise pollution in the practical engineering measurement, to dispose of the noise problem is very necessary for the measured time series analysis. Case 4 uses the SPCA method based on symplectic geometry to investigate the denoise of the vibration signals for rolling element fault (REF) from the CWRU database.
Symplectic geometry provides a new research idea for data analysis in practice. Although the symplectic geometry theory has been developed and applied on the nonlinear time series analysis, the related research based on symplectic geometry still needs to be further developed. Many future challenges in the research of symplectic geometry theory and various applications on a number of diverse aspects need to be developed furtherly. This chapter is only to provide a snapshot of some current trends and future challenges in the research of symplectic geometry theory on the time series analysis.
This work was supported by Shanghai “Science and technology innovation action plan” bio-medicine science and technology support project (Grant No. 19441907400).
The authors declare no conflict of interest.
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",metaTitle:"About Open Access",metaDescription:"Open access contributes to scientific excellence and integrity. It opens up research results to wider analysis. It allows research results to be reused for new discoveries. And it enables the multi-disciplinary research that is needed to solve global 21st century problems. Open access connects science with society. It allows the public to engage with research. To go behind the headlines. And look at the scientific evidence. And it enables policy makers to draw on innovative solutions to societal challenges.\n\nCarlos Moedas, the European Commissioner for Research Science and Innovation at the STM Annual Frankfurt Conference, October 2016.",metaKeywords:null,canonicalURL:"about-open-access",contentRaw:'[{"type":"htmlEditorComponent","content":"The Open Access publishing movement started in the early 2000s when academic leaders from around the world participated in the formation of the Budapest Initiative. They developed recommendations for an Open Access publishing process, “which has worked for the past decade to provide the public with unrestricted, free access to scholarly research—much of which is publicly funded. Making the research publicly available to everyone—free of charge and without most copyright and licensing restrictions—will accelerate scientific research efforts and allow authors to reach a larger number of readers” (reference: http://www.budapestopenaccessinitiative.org)
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\\n\\nIntechOpen is committed to ensuring the long-term preservation and the availability of all scholarly research we publish. We employ a variety of means to enable us to deliver on our commitments to the scientific community. Apart from preservation by the Croatian National Library (for publications prior to April 18, 2018) and the British Library (for publications after April 18, 2018), our entire catalogue is preserved in the CLOCKSS archive.
\\n"}]'},components:[{type:"htmlEditorComponent",content:'The Open Access publishing movement started in the early 2000s when academic leaders from around the world participated in the formation of the Budapest Initiative. They developed recommendations for an Open Access publishing process, “which has worked for the past decade to provide the public with unrestricted, free access to scholarly research—much of which is publicly funded. Making the research publicly available to everyone—free of charge and without most copyright and licensing restrictions—will accelerate scientific research efforts and allow authors to reach a larger number of readers” (reference: http://www.budapestopenaccessinitiative.org)
\n\nIntechOpen’s co-founders, both scientists themselves, created the company while undertaking research in robotics at Vienna University. Their goal was to spread research freely “for scientists, by scientists’ to the rest of the world via the Open Access publishing model. The company soon became a signatory of the Budapest Initiative, which currently has more than 1000 supporting organizations worldwide, ranging from universities to funders.
\n\nAt IntechOpen today, we are still as committed to working with organizations and people who care about scientific discovery, to putting the academic needs of the scientific community first, and to providing an Open Access environment where scientists can maximize their contribution to scientific advancement. By opening up access to the world’s scientific research articles and book chapters, we aim to facilitate greater opportunity for collaboration, scientific discovery and progress. We subscribe wholeheartedly to the Open Access definition:
\n\n“By “open access” to [peer-reviewed research literature], we mean its free availability on the public internet, permitting any users to read, download, copy, distribute, print, search, or link to the full texts of these articles, crawl them for indexing, pass them as data to software, or use them for any other lawful purpose, without financial, legal, or technical barriers other than those inseparable from gaining access to the internet itself. The only constraint on reproduction and distribution, and the only role for copyright in this domain, should be to give authors control over the integrity of their work and the right to be properly acknowledged and cited” (reference: http://www.budapestopenaccessinitiative.org)
\n\nOAI-PMH
\n\nAs a firm believer in the wider dissemination of knowledge, IntechOpen supports the Open Access Initiative Protocol for Metadata Harvesting (OAI-PMH Version 2.0). Read more
\n\nLicense
\n\nBook chapters published in edited volumes are distributed under the Creative Commons Attribution 3.0 Unported License (CC BY 3.0). IntechOpen upholds a very flexible Copyright Policy. There is no copyright transfer to the publisher and Authors retain exclusive copyright to their work. All Monographs/Compacts are distributed under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0). Read more
\n\nPeer Review Policies
\n\nAll scientific works are Peer Reviewed prior to publishing. Read more
\n\nOA Publishing Fees
\n\nThe Open Access publishing model employed by IntechOpen eliminates subscription charges and pay-per-view fees, enabling readers to access research at no cost. In order to sustain operations and keep our publications freely accessible we levy an Open Access Publishing Fee for manuscripts, which helps us cover the costs of editorial work and the production of books. Read more
\n\nDigital Archiving Policy
\n\nIntechOpen is committed to ensuring the long-term preservation and the availability of all scholarly research we publish. We employ a variety of means to enable us to deliver on our commitments to the scientific community. Apart from preservation by the Croatian National Library (for publications prior to April 18, 2018) and the British Library (for publications after April 18, 2018), our entire catalogue is preserved in the CLOCKSS archive.
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I am also a member of the team in charge for the supervision of Ph.D. students in the fields of development of silicon based planar waveguide sensor devices, study of inelastic electron tunnelling in planar tunnelling nanostructures for sensing applications and development of organotellurium(IV) compounds for semiconductor applications. I am a specialist in data analysis techniques and nanosurface structure. 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After obtaining a Master's degree in Mechanical Engineering, he continued his PhD studies in Robotics at the Vienna University of Technology. Here he worked as a robotic researcher with the university's Intelligent Manufacturing Systems Group as well as a guest researcher at various European universities, including the Swiss Federal Institute of Technology Lausanne (EPFL). During this time he published more than 20 scientific papers, gave presentations, served as a reviewer for major robotic journals and conferences and most importantly he co-founded and built the International Journal of Advanced Robotic Systems- world's first Open Access journal in the field of robotics. Starting this journal was a pivotal point in his career, since it was a pathway to founding IntechOpen - Open Access publisher focused on addressing academic researchers needs. Alex is a personification of IntechOpen key values being trusted, open and entrepreneurial. 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He is an expert in structural, absorptive, catalytic and photocatalytic properties, in structural organization and dynamic features of ionic liquids, in magnetic interactions between paramagnetic centers. The author or co-author of 3 books, over 200 articles and reviews in scientific journals and books. He is an actual member of the International EPR/ESR Society, European Society on Quantum Solar Energy Conversion, Moscow House of Scientists, of the Board of Moscow Physical Society.",institutionString:null,institution:{name:"Semenov Institute of Chemical Physics",country:{name:"Russia"}}},{id:"62389",title:"PhD.",name:"Ali Demir",middleName:null,surname:"Sezer",slug:"ali-demir-sezer",fullName:"Ali Demir Sezer",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/62389/images/3413_n.jpg",biography:"Dr. Ali Demir Sezer has a Ph.D. from Pharmaceutical Biotechnology at the Faculty of Pharmacy, University of Marmara (Turkey). 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