Γ\Gamma-convergence analysis of a generalized XYXY model: fractional vortices and string defects

We propose and analyze a generalized two dimensional $XY$ model, whose interaction potential has $n$ weighted wells, describing corresponding symmetries of the system. As the lattice spacing vanishes, we derive by $\Gamma$-convergence the discrete-to-continuum limit of this model. In the energy regime we deal with, the asymptotic ground states exhibit fractional vortices, connected by string defects. The $\Gamma$-limit takes into account both contributions, through a renormalized energy, depending on the configuration of fractional vortices, and a surface energy, proportional to the length of the strings. Our model describes in a simple way several topological singularities arising in Physics and Materials Science. Among them, disclinations and string defects in liquid crystals, fractional vortices and domain walls in micromagnetics, partial dislocations and stacking faults in crystal plasticity

Ground states of a two phase model with cross and self attractive interactions

We consider a variational model for two interacting species (or phases), subject to cross and self attractive forces. We show existence and several qualitative properties of minimizers. Depending on the strengths of the forces, different behaviors are possible: phase mixing or phase separation with nested or disjoint phases. In the case of Coulomb interaction forces, we characterize the ground state configurations

The #DNN-Verification Problem: Counting Unsafe Inputs for Deep Neural Networks

Deep Neural Networks are increasingly adopted in critical tasks that require a high level of safety, e.g., autonomous driving. While state-of-the-art verifiers can be employed to check whether a DNN is unsafe w.r.t. some given property (i.e., whether there is at least one unsafe input configuration), their yes/no output is not informative enough for other purposes, such as shielding, model selection, or training improvements. In this paper, we introduce the #DNN-Verification problem, which involves counting the number of input configurations of a DNN that result in a violation of a particular safety property. We analyze the complexity of this problem and propose a novel approach that returns the exact count of violations. Due to the #P-completeness of the problem, we also propose a randomized, approximate method that provides a provable probabilistic bound of the correct count while significantly reducing computational requirements. We present experimental results on a set of safety-critical benchmarks that demonstrate the effectiveness of our approximate method and evaluate the tightness of the bound.Comment: Accepted in the International Joint Conference on Artificial Intelligence (IJCAI), 2023. [Marzari and Corsi contributed equally

Ground states of a two phase model with cross and self attractive interactions

We consider a variational model for two interacting species (or phases), subject to cross and self attractive forces. We show existence and several qualitative properties of minimizers. Depending on the strengths of the forces, different behaviors are possible: phase mixing or phase separation with nested or disjoint phases. In the case of Coulomb interaction forces, we characterize the ground state configurations

Enumerating Safe Regions in Deep Neural Networks with Provable Probabilistic Guarantees

Identifying safe areas is a key point to guarantee trust for systems that are based on Deep Neural Networks (DNNs). To this end, we introduce the AllDNN-Verification problem: given a safety property and a DNN, enumerate the set of all the regions of the property input domain which are safe, i.e., where the property does hold. Due to the #P-hardness of the problem, we propose an efficient approximation method called epsilon-ProVe. Our approach exploits a controllable underestimation of the output reachable sets obtained via statistical prediction of tolerance limits, and can provide a tight (with provable probabilistic guarantees) lower estimate of the safe areas. Our empirical evaluation on different standard benchmarks shows the scalability and effectiveness of our method, offering valuable insights for this new type of verification of DNNs.Comment: Accepted at the 38th Annual AAAI Conference on Artificial Intelligence 202

A linear algorithm for string reconstruction in the reverse complement equivalence model

In the reverse complement equivalence model, it is not possible to distinguish a string from its reverse complement. We show that one can still reconstruct a string of length n, up to reverse complement, using a linear number of subsequence queries of bounded length. We first give the proof for strings over a binary alphabet, and then extend it to arbitrary finite alphabets. A simple information theoretic lower bound proves the number of queries to be asymptotically tight. Furthermore, our result is optimal w.r.t. the bound on the query length given in Erdos et al. (2006) [6]

Relationship between severe obesity and gut inflammation in children: what's next?

Background: Preliminary evidence suggests an association between obesity and gut inflammation. Aims: To evaluate the frequency of glucose abnormalities and their correlation with systemic and intestinal inflammation in severely obese children. Patients and Methods: Thirty-four children (25 males; median age 10.8 ± 3.4 yrs) with severe obesity (BMI >95%) were screened for diabetes with oral glucose tolerance test (OGTT), systemic inflammation with C-reactive protein (CRP) and gut inflammation with rectal nitric oxide (NO) and faecal calprotectin. Results: BMI ranged from 23 to 44 kg/m2, and BMI z-score between 2.08 e 4.93 (median 2.69 ± 0.53). Glucose abnormalities were documented in 71% of patients: type 2 diabetes in 29%, impaired fasting glucose (IFG) in 58%, and impaired glucose tolerance (IGT) in 37.5%. Thirty-one patients (91%) were hyperinsulinemic. CRP was increased in 73.5% with a correlation between BMI z-score and CRP (p 0.03). Faecal calprotectin was increased in 47% patients (mean 77 ± 68), and in 50% of children with abnormal glucose metabolism (mean 76 ± 68 ìg/g), with a correlation with increasing BMI z-score. NO was pathological in 88%, and in 87.5% of glucose impairment (mean 6.8 ± 5 ìM). Conclusions: In this study, the prevalence of glucose abnormalities in obese children is higher than in other series; furthermore, a correlation is present between markers of systemic and intestinal inflammation and glucose abnormalities

Hematopoietic reconstitution dynamics of mobilized- and bone marrow-derived human hematopoietic stem cells after gene therapy

Mobilized peripheral blood is increasingly used instead of bone marrow as a source of autologous hematopoietic stem/progenitor cells for ex vivo gene therapy. Here, we present an unplanned exploratory analysis evaluating the hematopoietic reconstitution kinetics, engraftment and clonality in 13 pediatric Wiskott-Aldrich syndrome patients treated with autologous lentiviral-vector transduced hematopoietic stem/progenitor cells derived from mobilized peripheral blood (n = 7), bone marrow (n = 5) or the combination of the two sources (n = 1). 8 out of 13 gene therapy patients were enrolled in an open-label, non-randomized, phase 1/2 clinical study (NCT01515462) and the remaining 5 patients were treated under expanded access programs. Although mobilized peripheral blood- and bone marrow- hematopoietic stem/progenitor cells display similar capability of being gene-corrected, maintaining the engineered grafts up to 3 years after gene therapy, mobilized peripheral blood-gene therapy group shows faster neutrophil and platelet recovery, higher number of engrafted clones and increased gene correction in the myeloid lineage which correlate with higher amount of primitive and myeloid progenitors contained in hematopoietic stem/progenitor cells derived from mobilized peripheral blood. In vitro differentiation and transplantation studies in mice confirm that primitive hematopoietic stem/progenitor cells from both sources have comparable engraftment and multilineage differentiation potential. Altogether, our analyses reveal that the differential behavior after gene therapy of hematopoietic stem/progenitor cells derived from either bone marrow or mobilized peripheral blood is mainly due to the distinct cell composition rather than functional differences of the infused cell products, providing new frames of references for clinical interpretation of hematopoietic stem/progenitor cell transplantation outcome.</p

Risk of Seizures in Children Receiving Busulphan-Containing Regimens for Stem Cell Transplantation

Busulphan (BU) is associated with neurotoxicity and risk of seizures. Hence, seizure prophylaxis is routinely utilized during BU administration for stem cell transplantation (SCT). We collected data on the incidence of seizures among children undergoing SCT in Italy. Fourteen pediatric transplantation centers agreed to report unselected data on children receiving BU as part of the conditioning regimen for SCT between 2005 and 2012. Data on 954 pediatric transplantation procedures were collected; of them, 66% of the patients received BU orally, and the remaining 34%, i.v. All the patients received prophylaxis of seizures, according to local protocols, consisting of different schedules and drugs. A total of 13 patients (1.3%) developed seizures; of them, 3 had a history of epilepsy (or other seizure-related pre-existing condition); 3 had documented brain lesions potentially causing seizures per se; 1 had febrile seizures, 1 severe hypo-osmolality. In the remaining 5 patients, seizures were considered not explained and, thus, potentially related to BU administration. The incidence of seizures in children receiving BU-containing regimen was very low (1.3%); furthermore, most of them had at least 1deither pre-existing or concurrentdassociated risk factor for seizures. 2014 American Society for Blood and Marrow Transplantation