Improving ADMMs for solving doubly nonnegative programs through dual factorization

Alternating direction methods of multipliers (ADMMs) are popular approaches to handle large scale semidefinite programs that gained attention during the past decade. In this paper, we focus on solving doubly nonnegative programs (DNN), which are semidefinite programs where the elements of the matrix variable are constrained to be nonnegative. Starting from two algorithms already proposed in the literature on conic programming, we introduce two new ADMMs by employing a factorization of the dual variable. It is well known that first order methods are not suitable to compute high precision optimal solutions, however an optimal solution of moderate precision often suffices to get high quality lower bounds on the primal optimal objective function value. We present methods to obtain such bounds by either perturbing the dual objective function value or by constructing a dual feasible solution from a dual approximate optimal solution. Both procedures can be used as a post-processing phase in our ADMMs. Numerical results for DNNs that are relaxations of the stable set problem are presented. They show the impact of using the factorization of the dual variable in order to improve the progress towards the optimal solution within an iteration of the ADMM. This decreases the number of iterations as well as the CPU time to solve the DNN to a given precision. The experiments also demonstrate that within a computationally cheap post-processing, we can compute bounds that are close to the optimal value even if the DNN was solved to moderate precision only. This makes ADMMs applicable also within a branch-and-bound algorithm

Discrete Particle Swarm Optimization for the minimum labelling Steiner tree problem

Particle Swarm Optimization is an evolutionary method inspired by the social behaviour of individuals inside swarms in nature. Solutions of the problem are modelled as members of the swarm which fly in the solution space. The evolution is obtained from the continuous movement of the particles that constitute the swarm submitted to the effect of the inertia and the attraction of the members who lead the swarm. This work focuses on a recent Discrete Particle Swarm Optimization for combinatorial optimization, called Jumping Particle Swarm Optimization. Its effectiveness is illustrated on the minimum labelling Steiner tree problem: given an undirected labelled connected graph, the aim is to find a spanning tree covering a given subset of nodes, whose edges have the smallest number of distinct labels

Linear-Time Zero-Knowledge Proofs for Arithmetic Circuit Satisfiability

We give computationally efficient zero-knowledge proofs of knowledge for arithmetic circuit satisfiability over a large field. For a circuit with N addition and multiplication gates, the prover only uses O(N)O(N) multiplications and the verifier only uses O(N)O(N) additions in the field. If the commitments we use are statistically binding, our zero-knowledge proofs have unconditional soundness, while if the commitments are statistically hiding we get computational soundness. Our zero-knowledge proofs also have sub-linear communication if the commitment scheme is compact. Our construction proceeds in three steps. First, we give a zero-knowledge proof for arithmetic circuit satisfiability in an ideal linear commitment model where the prover may commit to secret vectors of field elements, and the verifier can receive certified linear combinations of those vectors. Second, we show that the ideal linear commitment proof can be instantiated using error-correcting codes and non-interactive commitments. Finally, by choosing efficient instantiations of the primitives we obtain linear-time zero-knowledge proofs

Evaluation of the esthetic results of a 40-patient group treated surgically for dentoskeletal class III malocclusion

A dentoskeletal Class III malocclusion results in unesthetic alterations of the soft tissues, which may cause psychologic and interpersonal problems. Surgical treatment, if based on cephalometric evaluations alone, can result in inadequate correction of facial esthetics. The aim of this paper is to discuss the esthetic needs observed in surgical planning of a group of 40 Class III patients and to compare the presurgical esthetic parameters with those recorded in the sixth month of follow-up. To obtain the proper esthetic result and to restore proper stomatognathic functionality, surgical treatment planning required the integration and correction of skeletal cephalometric planning. In 24 of the 40 patients, the skeletal and esthetic planning were in agreement with each other. In the remaining 16 patients, the correction of skeletal planning with the esthetic planning was necessary to obtain the correct esthetic and functional restoration. In all patients, esthetic, radiographic, and functional analysis at the sixth month of follow-up revealed the restoration of correct facial esthetics in the vertical, transverse, and sagittal planes; no temporomandibular joint problems; and a high degree of personal satisfaction regarding the esthetic and functional result obtained, including improvements in social life and in masticatory function. Cephalometric indications should always be compared with esthetic clinical indications and, possibly, the skeletal planning must be corrected by the esthetic needs, so that esthetic and functional success can be reached at the same time

Soccer-related craniomaxillofacial injuries

The authors assessed the rate of craniomaxillofacial fractures in soccer and the areas where they occur, describing above all the injury pattern of this sport. Over a 5-year period (1995-2000) 46 cases of 329 with fractures associated with different sports activities have been surgically operated at the maxillofacial surgery department of the Policlinico "Umberto I" Hospital, University "La Sapienza" of Rome. All data collected have been selected on the basis of sex, age, anatomic site of the fracture, and the practiced sport. Information on injury patterns, severity, and play circumstances have been documented. The department examined 7 sports disciplines, but soccer was responsible for sports-related maxillofacial fractures in 34 of 46 cases (73.9%). All 34 fractures occurred to men. In soccer, the zygomatic and nasal regions are mainly involved. In fact the authors examined zygomatic fractures in 15 cases and nasal fractures in 10 cases. Direct contact between players generally causes soccer-related maxillofacial fractures: head-elbow impacts (21 cases) or head-head impacts (14 cases). The male:female ratio is 6.6:1, while the average age is 25 years for males and 23 years for females. In comparison with other sports (rugby, football, etc.) where physical contact occurs more frequently and the higher incidence of traumatic events justifies the use of protective measures, soccer is not a particularly violent sport. In soccer, maxillofacial traumas are caused by violent impacts between players that take place mainly when the ball is played with the forehead. In this moment there can be an elbow-head impact or a head-head impact. The authors believe that the low incidence of fractures, severity of the lesions, and discomfort caused by possible protective masks make their use unjustified. The data collected during this study witness that in soccer 21 of 34 cases of maxillofacial fractures are caused by elbow-head impacts. This fact suggests a preventive strategy against violent behavior in soccer play. Because the use of any sort of helmet proved impossible, the introduction of more severe penalties and a greater respect for the rules of the game by the players could reduce the percentage of impacts during matches. Impacts cause the most serious and frequent lesions in the maxillofacial region

Preliminary study of feasibility of an experiment looking for excited state double beta transitions in tin

An attempt to study the feasibility of a new experiment to search for double beta decay in $^{112}$Sn and $^{124}$Sn was carried out by using ultra-low background HPGe detector (244 cm$^{3}$) inside the Gran Sasso National Laboratory (LNGS) of the INFN (Italy). A small sample of natural Sn was examined for 2367.5 h. The radioactive contamination of the sample has been estimated. The data has also been considered to calculate the present sensitivity for the proposed search; half-life limits $\sim$ $10^{17} - 10^{18}$ years for $\beta^{+}$EC and EC-EC processes in $^{112}$Sn and $\sim$ $10^{18}$ years for $\beta^{-}\beta^{-}$ transition in $^{124}$Sn were measured. In the last section of the paper the enhancement of the sensitivity for a proposed experiment with larger mass to reach theoretically estimated values of half-lives is discussed.Comment: 20 pages, 11 figures, 4 tables, accepted for publication in NIMA (in press

Linear degenerations of flag varieties: partial flags, defining equations, and group actions

We continue, generalize and expand our study of linear degenerations of flag varieties from Cerulli Irelli et al. (Math Z 287(1–2):615–654, 2017). We realize partial flag varieties as quiver Grassmannians for equi-oriented type A quivers and construct linear degenerations by varying the corresponding quiver representation. We prove that there exists the deepest flat degeneration and the deepest flat irreducible degeneration: the former is the partial analogue of the mf-degenerate flag variety and the latter coincides with the partial PBW-degenerate flag variety. We compute the generating function of the number of orbits in the flat irreducible locus and study the natural family of line bundles on the degenerations from the flat irreducible locus. We also describe explicitly the reduced scheme structure on these degenerations and conjecture that similar results hold for the whole flat locus. Finally, we prove an analogue of the Borel–Weil theorem for the flat irreducible locus

Degenerate flag varieties: moment graphs and Schr\"oder numbers

We study geometric and combinatorial properties of the degenerate flag varieties of type A. These varieties are acted upon by the automorphism group of a certain representation of a type A quiver, containing a maximal torus T. Using the group action, we describe the moment graphs, encoding the zero- and one-dimensional T-orbits. We also study the smooth and singular loci of the degenerate flag varieties. We show that the Euler characteristic of the smooth locus is equal to the large Schr\"oder number and the Poincar\'e polynomial is given by a natural statistics counting the number of diagonal steps in a Schr\"oder path. As an application we obtain a new combinatorial description of the large and small Schr\"oder numbers and their q-analogues.Comment: 25 page

THE CLINICAL SIGNIFICANCE OF TWO DIFFERENT ELECTROMYOGRAPHY NORMALISATION TECHNIQUES IN PATIENTS WITH ANTERIOR CRUCIATE LIGAMENT INSTABILITY DURING TREADMILL WALKING

The purpose of this study is to investigate the clinical outcome of two normalisation techniques in detecting neuromuscular alterations of the quadriceps muscles between injured and non-injured patients diagnosed with ACL knee instability in their right knee during repeated gait cycles on a treadmill. The ensemble average muscle activity of the vastus lateralis and vastus medialis were normalised to either MVC or maximal activation during the gait cycle in eight male and female subjects. Results indicate that the EMG normalised to MVC was more sensitive in detecting differences in activation between the vastus lateralis and vastus medialis than the normalisation to maximal activity during repeated strides. This study indicates the importance of choosing the appropriate normalisation technique when seeking a clinical outcome measure

New limits on 2ε2\varepsilon, εβ+\varepsilon\beta^+ and 2β+2\beta^+ decay of 136^{136}Ce and 138^{138}Ce with deeply purified cerium sample

A search for double electron capture ($2\varepsilon$), electron capture with positron emission ($\varepsilon\beta^+$), and double positron emission $2\beta^+$) in $^{136}$Ce and $^{138}$Ce was realized with a 465 cm$^3$ ultra-low background HP Ge $\gamma$ spectrometer over 2299 h at the Gran Sasso underground laboratory. A 627 g sample of cerium oxide deeply purified by liquid-liquid extraction method was used as a source of $\gamma$ quanta expected in double $\beta$ decay of the cerium isotopes. New improved half-life limits were set on different modes and channels of double $\beta$ decay of $^{136}$Ce and $^{138}$Ce at the level of $T_{1/2}>10^{17}-10^{18}$ yr.Comment: 19 pages, 6 figures, 2 table