AUCTORES
Globalize your Research
Research Article
*Corresponding Author: TRS Moura, Federal University of Pará, Faculty of Physics, Interdisciplinary Innovation Laboratory – UFPA
Citation: JR Neyra, RS da Costa and TRS Moura (2019) Geometric Transitions Applied to Classification of Invasive Developmental Disorders.J Mathematical Methods in Engineering. 2(1): DOI: 10.31579/2690-0440/004
Copyright: © 2021 TRS Moura. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Received: 14 January 2021 | Accepted: 18 February 2021 | Published: 16 March 2021
Keywords: Random walks; Coupling. Diffusion
This manuscript has two purposes. The first objective is to fill a mathematical gap in the coupling formulation of two discrete random walk sets by constructing the matrix that quantifies the coupling for walking pairs. The second is to report the observation of two phenomena: withdrawal and approach. As the γ coupling intensity grows, we observe the formation of objects with distinct fractal dimensions, which characterize geometric transitions in random walks as a function of the coupling probability. We observed two geometric transitions. One transition occurs when the system transitions from clearance behavior to approach behavior, another occurs when random walkers are in the approach region. So, we make an analogy between random walks and pervasive developmental disorders, classifying a set of random walks as healthy and others with pervasive developmental disorder (PDD). We note that random walks have critical mutual influence, when γ=0.625 the coupling is maximum, where we notice the largest reduction in observations of the behavior of the individual with PDD. besides, for the set of random walks that represent the healthy set, even without PDD, their actions are influenced by individuals with PDD which may lead to a misdiagnosis.
In 1905, the random walk theory was born from K. Pearson's publication in the journal Nature. From this starting point, random walk theory has become a widely used tool for tackling problems in physics (Diniz et al., 2017), Economics (Masoliver et al., 2003), Engineering (McCarthy, 1993) (Klages, 2008), Biology and Medicine (Moura et al., 2018) (Cressoni et al., 2012).
In 2004, G.M. Schütz and S. Trimper discovered a new class of random walks. The class of random walks with memory. This random walk class has the feature of retrieving every step taken in the past with equal probability. This feature earned him the Elephant Random Walk model (ERW). Some other models were built from the ERW model, such as the Alzheimer random walk model (Cressoni et al., 2007), the Gaussian memory profile random walk model (Borges et al., 2012), the exponential memory profile random walk model (Alves et al., 2014), the exponential memory profile random walk model ( Moura et al., 2016) and the random walk model with binomial memory profile (Diniz et al., 2017).
In this class of random walks memory is an important feature. The memory is formed by a set of random variables: σt'
, in which t'
is the uniformly chosen time in the ERW model. Every instant of time t, the elephant's decision depends on its entire history retrieved from a uniform distribution. The probability of recovering a past action is 1t
with t
as the current time. At each moment the decision is recorded in memory, such property attributes a non-Markovian characteristic to the random walk. The walker walks one step to the right or one to the left, as in a one-dimensional Markovian random walk. The equation of stochastic evolution is
(1)
For a while
, the variable
takes the value
(
) when the walker performs a step to the right (left). Remembering that memory consists of a set of random variables
'
for the period of time
. The dynamics of this process occurs as follows:
a) In the period of time
a number '
of the set 1,2,…,t is randomly chosen with uniform probability 1/ t
b )
is determined stochastically by,
with probability
e
with probability
.
The first step is performed according to a specific rule. In the instant
; the walker is in position
, moves to the right
with probability of
to the left
with probability
. So it follows that the stochastic evolution equation is:
'
(2)
The parameter is the probability of the walker repeating a past action at the instant of time
. For
, the walker exhibits persistent behavior; for
the walker exhibits anti-persistent behavior; for
, the random walk is Markovian. There are two extreme points,
and
, for which random walks exhibit maximum behavior. At the point, the most anti-persistent behavior occurs; at the point:
,the most persistent behavior occurs: hiker moves deterministically. The class of random walks with memory exhibit strong dependence on the first step. The first step is macroscopically relevant and may influence the diffusion regimes measured by the Hurst exponent (Hurst et al., 1969).
The first moment of the position is:
(3)
In which
,
and
is the gamma function. The parameters
and
are set in the range
.
The second moment of the position is given by:
(4)
Observe that
the second moment, equation 4 depends linearly on and the diffusion is ordinary, for
diffusion is characterized as superdiffusive. In the point
the second moment is described by a logarithmic function of time (Schutz e Trimper, 2004).
Methodology
The ERW Two Dimensional Model
Two random ERW walkers, 1 and 2, walk along two distinct, perpendicular coordinate axes, just like:
and
, respectively. In the instant of time
, the position of the first walker is denoted by
. He recovers steps from his own memory as well as steps from the history of the second PAE, labeled
. The position of the i-nth random walker is quantified by the stochastic equation
(5)
With
. Microscopic dynamics follows the following rules:
(6)
(7)
The probability of the step of the i-nth that is walking in time t
,
, that comes from the spectrum of possibilities of the set
, is
(8)
In which the parameter
is probability of coupling of the i-nth elephant in relation to
k-nth elephant. So the probability of the first step is:
(9)
From equation 7 it is possible to calculate the probability of
, i.e.,
which is:
(10)
in which
e
.
The conditional displacement of the i-nth elephant is:
(11)
So from equation 11 we get the recursive relation of the first moment of position:
(12)
Another offset parameter, in this case for the first step, needs to be set as:
. Through this definition we can find the initial offset for the walking of index: i
(13)
The memory-coupled elephant random walk model was published in (Marquioni, 2019). Based on it, we reproduce the above results as a basis for building our model. Our model will use the memory coupling mechanisms introduced numerically and analytically in (Moura et al., 2018) and (Marquioni, 2019), in this exact order.
The Random Walk Model with PDD Characteristic
The PDD analogy for constructing the random walk model was first presented in (Moura et al, 2018). Others work emerged as a consequence, investigating new phenomenologies and introducing new mathematical tools (Moura-Ramos-Ramos, 2018), (Moura, 2019), (Marquioni, 2019).
In (Moura et al, 2018), PDD-type random walks were first introduced. In this model two random walks are unilaterally coupled, that is, one set of random walkers is influenced by the microscopic decisions of the other set of walkers, which are independent.
The first set of random walks is defined as independent, defined as the ERW model, which has the label of “Professor”. This model makes decisions from its own history. The second set of randoms, labeled “Student”, because it has the characteristic of maximum persistence in its microscopic decisions was defined as autistic, which can be influenced by its microscopic decisions according to its own memory or according to the memory of the ERW model. Decisions are retrieved from your memory (Professor's memory) with probability
). A superdiffusive regime was observed for all feedback parameter values in the range: p Є [0,1] with
. This phenomenon has never been observed in another model derived from the ERW randoms. For
walkers diffuse independently.
In (Moura-Ramos-Ramos, 2018), it was proposed to answer the following questions: How can the Professor influence and be influenced by the Student's microscopic decisions? If both learn from each other by making microscopic decisions that influence each other, what can we call a Professor process and Student process? To solve this apparent teaching-learning paradox, by construction, a bilateral memory coupling was performed. The Professor can learn (not learn) from the Student's decisions. Similarly, the Student can learn (not learn) from the Professor's decisions.
From the next section, we will use the mathematical formulation presented in (Marquioni, 2019), (Bercu, 2018) and (Bercu et al, 2019) to construct the coupling matrix that describes mutual influence of random walks. This is one of the main objective of this work.
The coupling
At this point, we will label “Professor” as set of random walks 1 and “Student” as set of random walks 2. Random walks 1 and 2 walk on different coordinate axes, the randoms with number 1 walk on axis
, perpendicular to the axis
where the 2 randoms 2 walk. Each walker's microscopic steps may influence each other's present state. The probability of walker decisions:
to be influenced by walker decisions:
is quantified by the coupling coefficient
.
Coupling coefficients are listed as follows:
(15)
According to equation 15, the first moment of position is given by the relation below:
(16)
According to equation 16, under the condition that there is a double coupling of 2 to 1, as well as 1 to 2. There are two cases to consider for coupling: the symmetrical case
and the non-symmetrical case
. In the symmetrical case walkers 1 and 2 have the same learning probability
. In the non-symmetrical case 1 or 2 may have probability functions that grow faster than the other. For example:
when walker 1 is more likely to modify his microscopic decisions according to walker 2's actions, and
otherwise. Let's address the case where
with
. Besides, let's vary a single feedback probability parameter by calling
com
, in which
.
Following these changes we rewrite the matrix equation of the first moment of position as:
(17)
We performed coupling between the aforementioned random walkers. The Professor with label 1 and the Student with label 2. We performed measurements of the first moment of Hurst position and exponent for various coupling intensities values: γ.
Discussion & Conclusion
We measured the effects of random walkers' coupling from fractal dimension measurements. To perform the measurements of the physical observables of the diffusive processes we proceeded with the ordinary analysis of the first moment of position
and measurements of the fractal dimension (D). In problems that can be modeled by random walks the diffusive regimes can be measured by the exponent H. The diffusive behavior can be quantified from the asymptotic scale law of the mean square deviation of position in relation to time that is
with i=1,2 related to walkers labeled 1 and 2. Where
is a constant of proportionality and
is the Hurst exponent of the i-nth walker. Diffusive regimes can be classified into sub-diffusive
, ordinary diffusive
and super diffusive
(Hurst et al., 1969). The fractal dimension is related to the Hurst exponent according to the following equation
, in which
is dimension in Euclidean space and
is the fractal dimension. The problem is modeled from a two-dimensional random walk (
).
In Figure 1, measurements of the difference in the first moment position of random walkers are displayed.
. The typical behavior of the first position moment for the random walkers 1 and 2 coupling problem, as a function of feedback and coupling:
and
, respectively; It is characterized by two phenomena. The phenomena of distance and approach. Measurements were made for the feedback parameter
coupling parameter varying in range:
. Our observations show that the clearance prevails over the approximation phenomenon to typical values of:
. In
, the distance appears with greater intensity, presenting average differences of the order of steps. As the coupling grows:
, The distance between walkers is reduced. In
, this average difference is reduced to the order of
steps. So from this point
, the approximation phenomenon prevails over the removal phenomenon, becoming stronger as
memory coupling becomes more intense.
Figure 1: Typical measurements of the average distance difference between walkers 1 and
for
. Measurements were made for coupling parameter varying in the range:
.
In Figure 2, fractal dimension measurements are displayed by setting the feedback parameters to a single value:
. The curves were obtained for the quantitative values of the feedback parameter equal to
and
and for the coupling parameter in the range of
. The fractal dimension curves of the random walkers were labeled as follows: the label RW1 for walker 1 and RW2 for the second walker. The curves at the top of figure 2 are for
. We note that the rapid convergence of the fractal dimensions occurs (
) even when the system is subjected to a slight increase in the coupling parameter :
. Insofar as:
gets stronger the coupling becomes, and the system no longer exhibits a characteristic behavior of the withdrawal phenomenon, transitioning to a behavior that characterizes the approach phenomenon. Approximation is a phenomenon characterized by fractal dimension measurements that converge to a single value for both random walkers.
. In
, random walkers with label 1 exhibit fractal dimension:
, characteristic of a dimensioned object between a two-dimensional object and a three-dimensional object, whereas the random walkers with label 2 have
of a two-dimensional object. As the coupling increases:
, the measures of D1
decrease and the
measures increase. After a variation in the coupling parameter, we note that the fractal dimensions of two random walkers converge to typical congruent values:
. At the bottom of Figure 2, for
we noted the same convergence behavior for fractal dimension measurements. We observed a behavioral change in the fractal dimension measurements of walker 1 in the
. The
measures show that there is an oscillation in the region of
, which is characterized by the increase of D1
, for a small increase γ>0
, of a two-dimensional object (
) for an object with dimension between two-dimensional and three-dimensional, with fractal dimension (
). Increasing the values of
, we noted the quantitative reduction of
. And also increasing
, in the region
, approximately we noted the convergence of fractal dimension measurements
. After the convergence in fractal dimension measurements, which we noted only by
, the dimension of random walks undergo a transition from a object with dimension
for a two-dimensional object
.
Figure 2: Fractal dimension measurements (
) walkers 1 and 2. Measurements were made for the feedback parameter equal to
and
with coupling parameter varying in the range of
. We use the label RW1 for walker 1 and RW2 for the second walker.
Conclusion
We proceed with the mathematical formulation of the coupling of two discrete random walk sets with two-dimensional coupling. We built the matrix that quantifies the coupling for discrete random walking pairs. From the coupling matrix, we perform numerical experiments to obtain the physical observables.
We perform numerical simulations of memory-coupled walks to answer the following question: How can the Professor influence and be influenced by the Student's microscopic decisions and vice versa? If both walkers learn from each other, how can we support the analogy of teaching and learning and call one process Professor and Student process? This apparent teaching-learning paradox was resolved by using the bilateral memory coupling technique (Moura-Ramos-Ramos, 2018).
We observed two physical phenomena related to coupling: the phenomenon of distance and approach. We noted that in the distance phenomenon, random walkers diffuse with less dependence, while greater variations in the coupling parameter are accompanied by greater dependence among random walkers. This dependence was quantified from the measurements of the first moment of position and fractal dimension of walkers 1 and 2. With a slight increase in the variation of the coupling parameter the system converges to the measurements of the first moment of position and to the fractal dimension measurements. More severe mental disorders are related to smaller fractal dimensions, while larger fractal dimensions can be used to classify less severe degrees of invasive developmental disorders. The distance and approach phenomena show rapid convergence with variations in the coupling probability. These phenomena carry the information that even a walkable individual, walker 1, in giving in and receiving information from an individual with some type of invasive developmental disorder, walker 2, can be influenced by its actions. The bond for mutual learning is quantified by the probability of coupling, which does not classify the reasons for justifying the intensity of coupling, we take as random because we do not know them, we can quantify them from the coupling parameter. We observed that walker 2, too, is influenced by walker 1's actions. Coupling has as a consequence the quantitative increase of fractal dimension for walker 1, which is associated with lower observations of the behavior of an individual with some invasive developmental disorder.
Conflict of Interest
There are no conflict of interests.
Acknowledgements
We thank the Federal University of Pará for financial support.
Clearly Auctoresonline and particularly Psychology and Mental Health Care Journal is dedicated to improving health care services for individuals and populations. The editorial boards' ability to efficiently recognize and share the global importance of health literacy with a variety of stakeholders. Auctoresonline publishing platform can be used to facilitate of optimal client-based services and should be added to health care professionals' repertoire of evidence-based health care resources.
Journal of Clinical Cardiology and Cardiovascular Intervention The submission and review process was adequate. However I think that the publication total value should have been enlightened in early fases. Thank you for all.
Journal of Women Health Care and Issues By the present mail, I want to say thank to you and tour colleagues for facilitating my published article. Specially thank you for the peer review process, support from the editorial office. I appreciate positively the quality of your journal.
Journal of Clinical Research and Reports I would be very delighted to submit my testimonial regarding the reviewer board and the editorial office. The reviewer board were accurate and helpful regarding any modifications for my manuscript. And the editorial office were very helpful and supportive in contacting and monitoring with any update and offering help. It was my pleasure to contribute with your promising Journal and I am looking forward for more collaboration.
We would like to thank the Journal of Thoracic Disease and Cardiothoracic Surgery because of the services they provided us for our articles. The peer-review process was done in a very excellent time manner, and the opinions of the reviewers helped us to improve our manuscript further. The editorial office had an outstanding correspondence with us and guided us in many ways. During a hard time of the pandemic that is affecting every one of us tremendously, the editorial office helped us make everything easier for publishing scientific work. Hope for a more scientific relationship with your Journal.
The peer-review process which consisted high quality queries on the paper. I did answer six reviewers’ questions and comments before the paper was accepted. The support from the editorial office is excellent.
Journal of Neuroscience and Neurological Surgery. I had the experience of publishing a research article recently. The whole process was simple from submission to publication. The reviewers made specific and valuable recommendations and corrections that improved the quality of my publication. I strongly recommend this Journal.
Dr. Katarzyna Byczkowska My testimonial covering: "The peer review process is quick and effective. The support from the editorial office is very professional and friendly. Quality of the Clinical Cardiology and Cardiovascular Interventions is scientific and publishes ground-breaking research on cardiology that is useful for other professionals in the field.
Thank you most sincerely, with regard to the support you have given in relation to the reviewing process and the processing of my article entitled "Large Cell Neuroendocrine Carcinoma of The Prostate Gland: A Review and Update" for publication in your esteemed Journal, Journal of Cancer Research and Cellular Therapeutics". The editorial team has been very supportive.
Testimony of Journal of Clinical Otorhinolaryngology: work with your Reviews has been a educational and constructive experience. The editorial office were very helpful and supportive. It was a pleasure to contribute to your Journal.
Dr. Bernard Terkimbi Utoo, I am happy to publish my scientific work in Journal of Women Health Care and Issues (JWHCI). The manuscript submission was seamless and peer review process was top notch. I was amazed that 4 reviewers worked on the manuscript which made it a highly technical, standard and excellent quality paper. I appreciate the format and consideration for the APC as well as the speed of publication. It is my pleasure to continue with this scientific relationship with the esteem JWHCI.
This is an acknowledgment for peer reviewers, editorial board of Journal of Clinical Research and Reports. They show a lot of consideration for us as publishers for our research article “Evaluation of the different factors associated with side effects of COVID-19 vaccination on medical students, Mutah university, Al-Karak, Jordan”, in a very professional and easy way. This journal is one of outstanding medical journal.
Dear Hao Jiang, to Journal of Nutrition and Food Processing We greatly appreciate the efficient, professional and rapid processing of our paper by your team. If there is anything else we should do, please do not hesitate to let us know. On behalf of my co-authors, we would like to express our great appreciation to editor and reviewers.
As an author who has recently published in the journal "Brain and Neurological Disorders". I am delighted to provide a testimonial on the peer review process, editorial office support, and the overall quality of the journal. The peer review process at Brain and Neurological Disorders is rigorous and meticulous, ensuring that only high-quality, evidence-based research is published. The reviewers are experts in their fields, and their comments and suggestions were constructive and helped improve the quality of my manuscript. The review process was timely and efficient, with clear communication from the editorial office at each stage. The support from the editorial office was exceptional throughout the entire process. The editorial staff was responsive, professional, and always willing to help. They provided valuable guidance on formatting, structure, and ethical considerations, making the submission process seamless. Moreover, they kept me informed about the status of my manuscript and provided timely updates, which made the process less stressful. The journal Brain and Neurological Disorders is of the highest quality, with a strong focus on publishing cutting-edge research in the field of neurology. The articles published in this journal are well-researched, rigorously peer-reviewed, and written by experts in the field. The journal maintains high standards, ensuring that readers are provided with the most up-to-date and reliable information on brain and neurological disorders. In conclusion, I had a wonderful experience publishing in Brain and Neurological Disorders. The peer review process was thorough, the editorial office provided exceptional support, and the journal's quality is second to none. I would highly recommend this journal to any researcher working in the field of neurology and brain disorders.
Dear Agrippa Hilda, Journal of Neuroscience and Neurological Surgery, Editorial Coordinator, I trust this message finds you well. I want to extend my appreciation for considering my article for publication in your esteemed journal. I am pleased to provide a testimonial regarding the peer review process and the support received from your editorial office. The peer review process for my paper was carried out in a highly professional and thorough manner. The feedback and comments provided by the authors were constructive and very useful in improving the quality of the manuscript. This rigorous assessment process undoubtedly contributes to the high standards maintained by your journal.
International Journal of Clinical Case Reports and Reviews. I strongly recommend to consider submitting your work to this high-quality journal. The support and availability of the Editorial staff is outstanding and the review process was both efficient and rigorous.
Thank you very much for publishing my Research Article titled “Comparing Treatment Outcome Of Allergic Rhinitis Patients After Using Fluticasone Nasal Spray And Nasal Douching" in the Journal of Clinical Otorhinolaryngology. As Medical Professionals we are immensely benefited from study of various informative Articles and Papers published in this high quality Journal. I look forward to enriching my knowledge by regular study of the Journal and contribute my future work in the field of ENT through the Journal for use by the medical fraternity. The support from the Editorial office was excellent and very prompt. I also welcome the comments received from the readers of my Research Article.
Dear Erica Kelsey, Editorial Coordinator of Cancer Research and Cellular Therapeutics Our team is very satisfied with the processing of our paper by your journal. That was fast, efficient, rigorous, but without unnecessary complications. We appreciated the very short time between the submission of the paper and its publication on line on your site.
I am very glad to say that the peer review process is very successful and fast and support from the Editorial Office. Therefore, I would like to continue our scientific relationship for a long time. And I especially thank you for your kindly attention towards my article. Have a good day!
"We recently published an article entitled “Influence of beta-Cyclodextrins upon the Degradation of Carbofuran Derivatives under Alkaline Conditions" in the Journal of “Pesticides and Biofertilizers” to show that the cyclodextrins protect the carbamates increasing their half-life time in the presence of basic conditions This will be very helpful to understand carbofuran behaviour in the analytical, agro-environmental and food areas. We greatly appreciated the interaction with the editor and the editorial team; we were particularly well accompanied during the course of the revision process, since all various steps towards publication were short and without delay".
I would like to express my gratitude towards you process of article review and submission. I found this to be very fair and expedient. Your follow up has been excellent. I have many publications in national and international journal and your process has been one of the best so far. Keep up the great work.
We are grateful for this opportunity to provide a glowing recommendation to the Journal of Psychiatry and Psychotherapy. We found that the editorial team were very supportive, helpful, kept us abreast of timelines and over all very professional in nature. The peer review process was rigorous, efficient and constructive that really enhanced our article submission. The experience with this journal remains one of our best ever and we look forward to providing future submissions in the near future.
I am very pleased to serve as EBM of the journal, I hope many years of my experience in stem cells can help the journal from one way or another. As we know, stem cells hold great potential for regenerative medicine, which are mostly used to promote the repair response of diseased, dysfunctional or injured tissue using stem cells or their derivatives. I think Stem Cell Research and Therapeutics International is a great platform to publish and share the understanding towards the biology and translational or clinical application of stem cells.
I would like to give my testimony in the support I have got by the peer review process and to support the editorial office where they were of asset to support young author like me to be encouraged to publish their work in your respected journal and globalize and share knowledge across the globe. I really give my great gratitude to your journal and the peer review including the editorial office.
I am delighted to publish our manuscript entitled "A Perspective on Cocaine Induced Stroke - Its Mechanisms and Management" in the Journal of Neuroscience and Neurological Surgery. The peer review process, support from the editorial office, and quality of the journal are excellent. The manuscripts published are of high quality and of excellent scientific value. I recommend this journal very much to colleagues.
Dr.Tania Muñoz, My experience as researcher and author of a review article in The Journal Clinical Cardiology and Interventions has been very enriching and stimulating. The editorial team is excellent, performs its work with absolute responsibility and delivery. They are proactive, dynamic and receptive to all proposals. Supporting at all times the vast universe of authors who choose them as an option for publication. The team of review specialists, members of the editorial board, are brilliant professionals, with remarkable performance in medical research and scientific methodology. Together they form a frontline team that consolidates the JCCI as a magnificent option for the publication and review of high-level medical articles and broad collective interest. I am honored to be able to share my review article and open to receive all your comments.
“The peer review process of JPMHC is quick and effective. Authors are benefited by good and professional reviewers with huge experience in the field of psychology and mental health. The support from the editorial office is very professional. People to contact to are friendly and happy to help and assist any query authors might have. Quality of the Journal is scientific and publishes ground-breaking research on mental health that is useful for other professionals in the field”.
Dear editorial department: On behalf of our team, I hereby certify the reliability and superiority of the International Journal of Clinical Case Reports and Reviews in the peer review process, editorial support, and journal quality. Firstly, the peer review process of the International Journal of Clinical Case Reports and Reviews is rigorous, fair, transparent, fast, and of high quality. The editorial department invites experts from relevant fields as anonymous reviewers to review all submitted manuscripts. These experts have rich academic backgrounds and experience, and can accurately evaluate the academic quality, originality, and suitability of manuscripts. The editorial department is committed to ensuring the rigor of the peer review process, while also making every effort to ensure a fast review cycle to meet the needs of authors and the academic community. Secondly, the editorial team of the International Journal of Clinical Case Reports and Reviews is composed of a group of senior scholars and professionals with rich experience and professional knowledge in related fields. The editorial department is committed to assisting authors in improving their manuscripts, ensuring their academic accuracy, clarity, and completeness. Editors actively collaborate with authors, providing useful suggestions and feedback to promote the improvement and development of the manuscript. We believe that the support of the editorial department is one of the key factors in ensuring the quality of the journal. Finally, the International Journal of Clinical Case Reports and Reviews is renowned for its high- quality articles and strict academic standards. The editorial department is committed to publishing innovative and academically valuable research results to promote the development and progress of related fields. The International Journal of Clinical Case Reports and Reviews is reasonably priced and ensures excellent service and quality ratio, allowing authors to obtain high-level academic publishing opportunities in an affordable manner. I hereby solemnly declare that the International Journal of Clinical Case Reports and Reviews has a high level of credibility and superiority in terms of peer review process, editorial support, reasonable fees, and journal quality. Sincerely, Rui Tao.
Clinical Cardiology and Cardiovascular Interventions I testity the covering of the peer review process, support from the editorial office, and quality of the journal.
Clinical Cardiology and Cardiovascular Interventions, we deeply appreciate the interest shown in our work and its publication. It has been a true pleasure to collaborate with you. The peer review process, as well as the support provided by the editorial office, have been exceptional, and the quality of the journal is very high, which was a determining factor in our decision to publish with you.
The peer reviewers process is quick and effective, the supports from editorial office is excellent, the quality of journal is high. I would like to collabroate with Internatioanl journal of Clinical Case Reports and Reviews journal clinically in the future time.
Clinical Cardiology and Cardiovascular Interventions, I would like to express my sincerest gratitude for the trust placed in our team for the publication in your journal. It has been a true pleasure to collaborate with you on this project. I am pleased to inform you that both the peer review process and the attention from the editorial coordination have been excellent. Your team has worked with dedication and professionalism to ensure that your publication meets the highest standards of quality. We are confident that this collaboration will result in mutual success, and we are eager to see the fruits of this shared effort.
Dear Dr. Jessica Magne, Editorial Coordinator 0f Clinical Cardiology and Cardiovascular Interventions, I hope this message finds you well. I want to express my utmost gratitude for your excellent work and for the dedication and speed in the publication process of my article titled "Navigating Innovation: Qualitative Insights on Using Technology for Health Education in Acute Coronary Syndrome Patients." I am very satisfied with the peer review process, the support from the editorial office, and the quality of the journal. I hope we can maintain our scientific relationship in the long term.
Dear Monica Gissare, - Editorial Coordinator of Nutrition and Food Processing. ¨My testimony with you is truly professional, with a positive response regarding the follow-up of the article and its review, you took into account my qualities and the importance of the topic¨.
Dear Dr. Jessica Magne, Editorial Coordinator 0f Clinical Cardiology and Cardiovascular Interventions, The review process for the article “The Handling of Anti-aggregants and Anticoagulants in the Oncologic Heart Patient Submitted to Surgery” was extremely rigorous and detailed. From the initial submission to the final acceptance, the editorial team at the “Journal of Clinical Cardiology and Cardiovascular Interventions” demonstrated a high level of professionalism and dedication. The reviewers provided constructive and detailed feedback, which was essential for improving the quality of our work. Communication was always clear and efficient, ensuring that all our questions were promptly addressed. The quality of the “Journal of Clinical Cardiology and Cardiovascular Interventions” is undeniable. It is a peer-reviewed, open-access publication dedicated exclusively to disseminating high-quality research in the field of clinical cardiology and cardiovascular interventions. The journal's impact factor is currently under evaluation, and it is indexed in reputable databases, which further reinforces its credibility and relevance in the scientific field. I highly recommend this journal to researchers looking for a reputable platform to publish their studies.
Dear Editorial Coordinator of the Journal of Nutrition and Food Processing! "I would like to thank the Journal of Nutrition and Food Processing for including and publishing my article. The peer review process was very quick, movement and precise. The Editorial Board has done an extremely conscientious job with much help, valuable comments and advices. I find the journal very valuable from a professional point of view, thank you very much for allowing me to be part of it and I would like to participate in the future!”
Dealing with The Journal of Neurology and Neurological Surgery was very smooth and comprehensive. The office staff took time to address my needs and the response from editors and the office was prompt and fair. I certainly hope to publish with this journal again.Their professionalism is apparent and more than satisfactory. Susan Weiner
