A Generalized Sylvester-Gallai Type Theorem for Quadratic Polynomials

In this work we prove a version of the Sylvester-Gallai theorem for quadratic polynomials that takes us one step closer to obtaining a deterministic polynomial time algorithm for testing zeroness of ?^{[3]}???^{[2]} circuits. Specifically, we prove that if a finite set of irreducible quadratic polynomials ? satisfy that for every two polynomials Q?,Q? ? ? there is a subset ? ? ?, such that Q?,Q? ? ? and whenever Q? and Q? vanish then ?_{Q_i??} Q_i vanishes, then the linear span of the polynomials in ? has dimension O(1). This extends the earlier result [Amir Shpilka, 2019] that showed a similar conclusion when |?| = 1. An important technical step in our proof is a theorem classifying all the possible cases in which a product of quadratic polynomials can vanish when two other quadratic polynomials vanish. I.e., when the product is in the radical of the ideal generated by the two quadratics. This step extends a result from [Amir Shpilka, 2019] that studied the case when one quadratic polynomial is in the radical of two other quadratics

Lower Bounds on Stabilizer Rank

The stabilizer rank of a quantum state ? is the minimal r such that |?? = ?_{j = 1}^r c_j |?_j? for c_j ? ? and stabilizer states ?_j. The running time of several classical simulation methods for quantum circuits is determined by the stabilizer rank of the n-th tensor power of single-qubit magic states. We prove a lower bound of ?(n) on the stabilizer rank of such states, improving a previous lower bound of ?(?n) of Bravyi, Smith and Smolin [Bravyi et al., 2016]. Further, we prove that for a sufficiently small constant ?, the stabilizer rank of any state which is ?-close to those states is ?(?n/log n). This is the first non-trivial lower bound for approximate stabilizer rank. Our techniques rely on the representation of stabilizer states as quadratic functions over affine subspaces of ???, and we use tools from analysis of boolean functions and complexity theory. The proof of the first result involves a careful analysis of directional derivatives of quadratic polynomials, whereas the proof of the second result uses Razborov-Smolensky low degree polynomial approximations and correlation bounds against the majority function

BPM: Blended Piecewise Moebius Maps

We propose a novel Moebius interpolator that takes as an input a discrete map between the vertices of two planar triangle meshes, and outputs a smooth map on the input domain. The output map interpolates the discrete map, is continuous between triangles, and has low quasi-conformal distortion when the input map is discrete conformal. Our map leads to considerably smoother texture transfer compared to the alternatives, even on very coarse triangulations. Furthermore, our approach has a closed-form expression, is local, applicable to any discrete map, and leads to smooth results even for extreme deformations. Finally, by working with local intrinsic coordinates, our approach is easily generalizable to discrete maps between a surface triangle mesh and a planar mesh, i.e., a planar parameterization. We compare our method with existing approaches, and demonstrate better texture transfer results, and lower quasi-conformal errors

Hyperbaric Oxygen Therapy Can Induce Neuroplasticity and Significant Clinical Improvement in Patients Suffering From Fibromyalgia With a History of Childhood Sexual Abuse—Randomized Controlled Trial

Background: Fibromyalgia syndrome (FMS), a condition considered to represent a prototype of central sensitization syndrome, can be induced by different triggers including childhood sexual abuse (CSA). Recent studies have demonstrated hyperbaric oxygen therapy (HBOT) can induce neuroplasticity and improve clinical outcome of FMS. The aim of the current study was to evaluate the effect of HBOT on patients suffering from FMS with a history of CSA.Materials and methods: A prospective randomized clinical trial conducted between July 2015 and November 2017 included women with a history of CSA who fulfilled fibromyalgia diagnosis criteria for at least 5 years prior to inclusion. Included participants (N = 30) were randomly assigned to treatment group, treated with 60 HBOT sessions and a control/crossover group received psychotherapy. After the control period, the control/crossover group was crossed to HBOT. Clinical outcomes were assessed using FMS questioners, post-traumatic stress disorder (PTSD) questioners and quality of life questioners. Objective outcome were assessed using brain function and structure imaging.Findings: Following HBOT, there was a significant improvement in all FMS questionnaires (widespread pain index, Fibromyalgia symptoms severity scale, Fibromyalgia functional impairment), most domains of quality of life, PTSD symptoms and psychological distress. The same significant improvements were demonstrated in the control following crossover to HBOT. Following HBOT, brain SPECT imaging demonstrated significant increase in brain activity in the prefrontal cortex, orbital frontal cortex, and subgenual area (p < 0.05). Brain microstructure improvement was seen by MRI-DTI in the anterior thalamic radiation (p = 0.0001), left Insula (p = 0.001), and the right Thalamus (p = 0.001).Conclusion: HBOT induced significant clinical improvement that correlates with improved brain functionality and brain microstructure in CSA related FMS patients.Trial Registration:www.Clinicaltrials.gov, identifier: NCT03376269. url: https://clinicaltrials.gov/show/NCT0337626

Explainable automated recognition of emotional states from canine facial expressions: the case of positive anticipation and frustration.

In animal research, automation of affective states recognition has so far mainly addressed pain in a few species. Emotional states remain uncharted territories, especially in dogs, due to the complexity of their facial morphology and expressions. This study contributes to fill this gap in two aspects. First, it is the first to address dog emotional states using a dataset obtained in a controlled experimental setting, including videos from (n = 29) Labrador Retrievers assumed to be in two experimentally induced emotional states: negative (frustration) and positive (anticipation). The dogs' facial expressions were measured using the Dogs Facial Action Coding System (DogFACS). Two different approaches are compared in relation to our aim: (1) a DogFACS-based approach with a two-step pipeline consisting of (i) a DogFACS variable detector and (ii) a positive/negative state Decision Tree classifier; (2) An approach using deep learning techniques with no intermediate representation. The approaches reach accuracy of above 71% and 89%, respectively, with the deep learning approach performing better. Secondly, this study is also the first to study explainability of AI models in the context of emotion in animals. The DogFACS-based approach provides decision trees, that is a mathematical representation which reflects previous findings by human experts in relation to certain facial expressions (DogFACS variables) being correlates of specific emotional states. The deep learning approach offers a different, visual form of explainability in the form of heatmaps reflecting regions of focus of the network's attention, which in some cases show focus clearly related to the nature of particular DogFACS variables. These heatmaps may hold the key to novel insights on the sensitivity of the network to nuanced pixel patterns reflecting information invisible to the human eye

Brain and Mind Integration: Childhood Sexual Abuse Survivors Experiencing Hyperbaric Oxygen Treatment and Psychotherapy Concurrently

Due to evidence that traumatic experience impacts the brain, the body (concerning sensory sensitivity), and the mind, a recent study that attempted to answer the question of whether the effects of CSA can be reversed by using a multidisciplinary approach consisting of dual treatments: hyperbaric & psychotherapy, was conducted. Its results showed that in addition to improvement of brain functionality, symptoms of distress were significantly reduced. The current paper aims to present the process as experienced by the 40 female childhood sexual abuse survivor participants. Data included participants' daily journals and drawings, and participants' summaries presented verbally and written, 6-months after the study ended. A phenomenological analysis was used. Results showed three phases, the initial phase—remembering the trauma from both physical and cognitive aspects, the second phase—physiological relaxation as well as positive memories emerge; and, the third phase—bouncing back to life. The results are discussed in light of the study theoretical model and Lev-Wiesel (2015) childhood sexual abuse conceptualization

Effects of anxiety on canine movement in dog-robot interactions.

Canine behavioral disorders, such as various forms of fear and anxiety, are a major threat for the well-being of dogs and their owners. They are also the main cause for dog abandonment and relinquishment to shelters. Timely diagnosis and treatment of such problems is a complex task, requiring extensive behavioral expertise. Accurate classification of pathological behavior requires information on the dog's reactions to environmental stimuli. Such information is typically self-reported by the animal's owner, posing a threat to its accuracy and correctness. Simple robots have been used as controllable stimuli for evoking particular canine behaviors, leading to the increasing interest in dog-robot interactions (DRIs). We explore the use of DRIs as a tool for the assessment of canine behavioral disorders. More concretely, we ask in what ways disorders such as anxiety may be reflected in the way dogs interact with a robot. To this end, we performed an exploratory study, recording DRIs for a group of 20 dogs, consisting of 10 dogs diagnosed by a behavioral expert veterinarian with deprivation syndrome, a form of phobia/anxiety caused by inadequate development conditions, and 10 healthy control dogs. Pathological dogs moved significantly less than the control group during these interactions