Some Exact Results on the Ultrametric Overlap Distribution in Mean Field Spin Glass Models (I)

The mean field spin glass model is analyzed by a combination of mathematically rigororous methods and a powerful Ansatz. The method exploited is general, and can be applied to others disordered mean field models such as, e.g., neural networks. It is well known that the probability measure of overlaps among replicas carries the whole physical content of these models. A functional order parameter of Parisi type is introduced by rigorous methods, according to previous works by F. Guerra. By the Ansatz that the functional order parameter is the correct order parameter of the model, we explicitly find the full overlap distribution. The physical interpretation of the functional order parameter is obtained, and ultrametricity of overlaps is derived as a natural consequence of a branching diffusion process. It is shown by explicit construction that ultrametricity of the 3-replicas overlap distribution together with the Ghirlanda-Guerra relations determines the distribution of overlaps among s replicas, for any s, in terms of the one-overlap distribution.Comment: 17 pages, submitted to Euro. Phys. Jou. B Direc

Generalized Strong Preservation by Abstract Interpretation

Standard abstract model checking relies on abstract Kripke structures which approximate concrete models by gluing together indistinguishable states, namely by a partition of the concrete state space. Strong preservation for a specification language L encodes the equivalence of concrete and abstract model checking of formulas in L. We show how abstract interpretation can be used to design abstract models that are more general than abstract Kripke structures. Accordingly, strong preservation is generalized to abstract interpretation-based models and precisely related to the concept of completeness in abstract interpretation. The problem of minimally refining an abstract model in order to make it strongly preserving for some language L can be formulated as a minimal domain refinement in abstract interpretation in order to get completeness w.r.t. the logical/temporal operators of L. It turns out that this refined strongly preserving abstract model always exists and can be characterized as a greatest fixed point. As a consequence, some well-known behavioural equivalences, like bisimulation, simulation and stuttering, and their corresponding partition refinement algorithms can be elegantly characterized in abstract interpretation as completeness properties and refinements

Generalizing the Paige-Tarjan Algorithm by Abstract Interpretation

The Paige and Tarjan algorithm (PT) for computing the coarsest refinement of a state partition which is a bisimulation on some Kripke structure is well known. It is also well known in model checking that bisimulation is equivalent to strong preservation of CTL, or, equivalently, of Hennessy-Milner logic. Drawing on these observations, we analyze the basic steps of the PT algorithm from an abstract interpretation perspective, which allows us to reason on strong preservation in the context of generic inductively defined (temporal) languages and of possibly non-partitioning abstract models specified by abstract interpretation. This leads us to design a generalized Paige-Tarjan algorithm, called GPT, for computing the minimal refinement of an abstract interpretation-based model that strongly preserves some given language. It turns out that PT is a straight instance of GPT on the domain of state partitions for the case of strong preservation of Hennessy-Milner logic. We provide a number of examples showing that GPT is of general use. We first show how a well-known efficient algorithm for computing stuttering equivalence can be viewed as a simple instance of GPT. We then instantiate GPT in order to design a new efficient algorithm for computing simulation equivalence that is competitive with the best available algorithms. Finally, we show how GPT allows to compute new strongly preserving abstract models by providing an efficient algorithm that computes the coarsest refinement of a given partition that strongly preserves the language generated by the reachability operator.Comment: Keywords: Abstract interpretation, abstract model checking, strong preservation, Paige-Tarjan algorithm, refinement algorith

Coexisting attractors and chaotic canard explosions in a slow-fast optomechanical system

The multiple time scale dynamics induced by radiation pressure and photothermal effects in a high-finesse optomechanical resonator is experimentally studied. At difference with two-dimensional slow-fast systems, the transition from the quasiharmonic to the relaxational regime occurs via chaotic canard explosions, where large-amplitude relaxation spikes are separated by an irregular number of subthreshold oscillations. We also show that this regime coexists with other periodic attractors, on which the trajectories evolve on a substantially faster time scale. The experimental results are reproduced and analyzed by means of a detailed physical model of our system.Comment: 8 pages; 6 figure

Chaotically spiking attractors in suspended mirror optical cavities

A high-finesse suspended mirror Fabry-Perot cavity is experimentally studied in a regime where radiation pressure and photothermal effect are both relevant. The competition between these phenomena, operating at different time scales, produces unobserved dynamical scenarios where an initial Hopf instability is followed by the birth of small-amplitude chaotic attractors which erratically but deterministically trigger optical spikes. The observed dynamical regimes are well reproduced by a detailed physical model of the system

Vat. copt. 57: A Codicological, Literary, and Paratextual Analysis

MS Vatican City, Biblioteca Apostolica Vaticana Vat. copt. 57, a collection of homi- lies attributed to John Chrysostom in Bohairic Coptic, poses a number of challenges to scholars. Questions such as, Can we identify the texts, and what is their rela- tionship to their Greek models? Can we know who the copyist(s) was or were? are approached by a team of scholars in a collaborative stud

SU(N) Meander Determinants

We propose a generalization of meanders, i.e., configurations of non-selfintersecting loops crossing a line through a given number of points, to SU(N). This uses the reformulation of meanders as pairs of reduced elements of the Temperley-Lieb algebra, a SU(2)-related quotient of the Hecke algebra, with a natural generalization to SU(N). We also derive explicit formulas for SU(N) meander determinants, defined as the Gram determinants of the corresponding bases of the Hecke algebra.Comment: TeX using harvmac.tex and epsf.tex, 60 pages (l-mode), 5 figure

Treatment of Adult Patients with Relapsed/Refractory B-Cell Philadelphia-Negative Acute Lymphoblastic Leukemia

The majority of adult patients affected by B-cell acute lymphoblastic leukemia (B-ALL) will relapse after an initial response, while approximately 20% will display primary resistant disease. Patients suffering from relapsed/refractory B-ALL have a very poor outcome. Allogeneic hematopoietic cell transplantation (HCT) still represents the only curative approach, but is not so frequently feasible, because of patient’s fitness, donor availability, and the ability to achieve a remission prior to HCT. The estimated remission rates with conventional cytotoxic agents are around 30%, but they are short-lived. These disappointing results led to the introduction of new immunologic-based treatments—blinatumomab and inotuzumab. They produced a substantial improvement in terms of response rates, with the ability, in most cases, to induce a minimal residual disease (MRD)-negative status. Similarly, T cells engineered to express a CD19-specific chimeric antigen receptor (CAR-T) have yielded sensational results among patients with relapsed/refractory B-ALL, with unexpectedly high MRD-negative complete remissions rates. However, the first studies looking at long-term outcomes after CAR-T infusions told us that a significant fraction of such responses are not durable, and may benefit from a consolidation approach such as an allogeneic HCT