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

Challenges and advanced concepts for the assessment of learning and memory function in mice

The mechanisms underlying the formation and retrieval of memories are still an active area of research and discussion. Manifold models have been proposed and refined over the years, with most assuming a dichotomy between memory processes involving non-conscious and conscious mechanisms. Despite our incomplete understanding of the underlying mechanisms, tests of memory and learning count among the most performed behavioral experiments. Here, we will discuss available protocols for testing learning and memory using the example of the most prevalent animal species in research, the laboratory mouse. A wide range of protocols has been developed in mice to test, e.g., object recognition, spatial learning, procedural memory, sequential problem solving, operant- and fear conditioning, and social recognition. Those assays are carried out with individual subjects in apparatuses such as arenas and mazes, which allow for a high degree of standardization across laboratories and straightforward data interpretation but are not without caveats and limitations. In animal research, there is growing concern about the translatability of study results and animal welfare, leading to novel approaches beyond established protocols. Here, we present some of the more recent developments and more advanced concepts in learning and memory testing, such as multi-step sequential lockboxes, assays involving groups of animals, as well as home cage-based assays supported by automated tracking solutions; and weight their potential and limitations against those of established paradigms. Shifting the focus of learning tests from the classical experimental chamber to settings which are more natural for rodents comes with a new set of challenges for behavioral researchers, but also offers the opportunity to understand memory formation and retrieval in a more conclusive way than has been attainable with conventional test protocols. We predict and embrace an increase in studies relying on methods involving a higher degree of automatization, more naturalistic- and home cage-based experimental setting as well as more integrated learning tasks in the future. We are confident these trends are suited to alleviate the burden on animal subjects and improve study designs in memory research

Wall-Crossing from Boltzmann Black Hole Halos

A key question in the study of N=2 supersymmetric string or field theories is to understand the decay of BPS bound states across walls of marginal stability in the space of parameters or vacua. By representing the potentially unstable bound states as multi-centered black hole solutions in N=2 supergravity, we provide two fully general and explicit formulae for the change in the (refined) index across the wall. The first, "Higgs branch" formula relies on Reineke's results for invariants of quivers without oriented loops, specialized to the Abelian case. The second, "Coulomb branch" formula results from evaluating the symplectic volume of the classical phase space of multi-centered solutions by localization. We provide extensive evidence that these new formulae agree with each other and with the mathematical results of Kontsevich and Soibelman (KS) and Joyce and Song (JS). The main physical insight behind our results is that the Bose-Fermi statistics of individual black holes participating in the bound state can be traded for Maxwell-Boltzmann statistics, provided the (integer) index \Omega(\gamma) of the internal degrees of freedom carried by each black hole is replaced by an effective (rational) index \bar\Omega(\gamma)= \sum_{m|\gamma} \Omega(\gamma/m)/m^2. A similar map also exists for the refined index. This observation provides a physical rationale for the appearance of the rational Donaldson-Thomas invariant \bar\Omega(\gamma) in the works of KS and JS. The simplicity of the wall crossing formula for rational invariants allows us to generalize the "semi-primitive wall-crossing formula" to arbitrary decays of the type \gamma\to M\gamma_1+N\gamma_2 with M=2,3.Comment: 71 pages, 1 figure; v3: changed normalisation of symplectic form 3.22, corrected 3.35, other cosmetic change

Multiple infarcted regenerative nodules in liver cirrhosis after decompensation of cirrhosis: a case series

These patients showed focal liver lesions, to be considered in the differential diagnosis of cirrhotic livers. Infarcted regenerative nodules may be underdiagnosed in patients with decompensation of cirrhosis. In order to differentiate these lesions from malignant tumors, serial imaging seems to be helpful. However, the main differential diagnosis should be an abscess. It is important to know the wide spectrum of image appearances of these lesions. Hypotension can lead to a reduction of portal and arterial liver flow. Since variceal bleeding or septic shock can induce hypotension - as observed in our patients - we conclude that this leads to infarction of such nodules

Treatment of millet crop plant (Sorghum bicolor) with the entomopathogenic fungus (Beauveria bassiana) to combat infestation by the stem borer, Chilo partellus Swinhoe (Lepidoptera: Pyralidae)

Experiments were done to test if Beauveria bassiana can become an endophyte in sorghum and confer protection from stem borer. Four-week-old sorghum seedlings were treated with B. bassiana. The plants were examined for endophytic presence of B. bassiana, 30 and 60 days after treatment. Stem cultures from treated plants showed growth of B. bassiana. PCR amplification using fungal specific primers for a conserved region of β tubulin gene yielded identical 360 bp products from both B. bassiana and treated sorghum plants. In a subsequent experiment, B. bassiana treated and untreated (control) sorghum plants were artificially infested with stem borer (Chilo partellus) larvae 15 days post treatment and the extent of damage was compared. About 40% of the control plants developed dead heart while no plant in the B. bassiana treated plot did. In the surviving control plants, stem tunneling by shoot borer was significantly higher compared to B. bassiana treated sorghum plants

Challenges and advanced concepts for the assessment of learning and memory function in mice

The mechanisms underlying the formation and retrieval of memories are still an active area of research and discussion. Manifold models have been proposed and refined over the years, with most assuming a dichotomy between memory processes involving non-conscious and conscious mechanisms. Despite our incomplete understanding of the underlying mechanisms, tests of memory and learning count among the most performed behavioral experiments. Here, we will discuss available protocols for testing learning and memory using the example of the most prevalent animal species in research, the laboratory mouse. A wide range of protocols has been developed in mice to test, e.g., object recognition, spatial learning, procedural memory, sequential problem solving, operant- and fear conditioning, and social recognition. Those assays are carried out with individual subjects in apparatuses such as arenas and mazes, which allow for a high degree of standardization across laboratories and straightforward data interpretation but are not without caveats and limitations. In animal research, there is growing concern about the translatability of study results and animal welfare, leading to novel approaches beyond established protocols. Here, we present some of the more recent developments and more advanced concepts in learning and memory testing, such as multi-step sequential lockboxes, assays involving groups of animals, as well as home cage-based assays supported by automated tracking solutions; and weight their potential and limitations against those of established paradigms. Shifting the focus of learning tests from the classical experimental chamber to settings which are more natural for rodents comes with a new set of challenges for behavioral researchers, but also offers the opportunity to understand memory formation and retrieval in a more conclusive way than has been attainable with conventional test protocols. We predict and embrace an increase in studies relying on methods involving a higher degree of automatization, more naturalistic- and home cage-based experimental setting as well as more integrated learning tasks in the future. We are confident these trends are suited to alleviate the burden on animal subjects and improve study designs in memory research

An extensible framework for multicore response time analysis

In this paper, we introduce a multicore response time analysis (MRTA) framework, which decouples response time analysis from a reliance on context independent WCET values. Instead, the analysis formulates response times directly from the demands placed on different hardware resources. The MRTA framework is extensible to different multicore architectures, with a variety of arbitration policies for the common interconnects, and different types and arrangements of local memory. We instantiate the framework for single level local data and instruction memories (cache or scratchpads), for a variety of memory bus arbitration policies, including: Round-Robin, FIFO, Fixed-Priority, Processor-Priority, and TDMA, and account for DRAM refreshes. The MRTA framework provides a general approach to timing verification for multicore systems that is parametric in the hardware configuration and so can be used at the architectural design stage to compare the guaranteed levels of real-time performance that can be obtained with different hardware configurations. We use the framework in this way to evaluate the performance of multicore systems with a variety of different architectural components and policies. These results are then used to compose a predictable architecture, which is compared against a reference architecture designed for good average-case behaviour. This comparison shows that the predictable architecture has substantially better guaranteed real-time performance, with the precision of the analysis verified using cycle-accurate simulation

Atomic structures of TDP-43 LCD segments and insights into reversible or pathogenic aggregation.

The normally soluble TAR DNA-binding protein 43 (TDP-43) is found aggregated both in reversible stress granules and in irreversible pathogenic amyloid. In TDP-43, the low-complexity domain (LCD) is believed to be involved in both types of aggregation. To uncover the structural origins of these two modes of β-sheet-rich aggregation, we have determined ten structures of segments of the LCD of human TDP-43. Six of these segments form steric zippers characteristic of the spines of pathogenic amyloid fibrils; four others form LARKS, the labile amyloid-like interactions characteristic of protein hydrogels and proteins found in membraneless organelles, including stress granules. Supporting a hypothetical pathway from reversible to irreversible amyloid aggregation, we found that familial ALS variants of TDP-43 convert LARKS to irreversible aggregates. Our structures suggest how TDP-43 adopts both reversible and irreversible β-sheet aggregates and the role of mutation in the possible transition of reversible to irreversible pathogenic aggregation

How to Compute Worst-Case Execution Time by Optimization Modulo Theory and a Clever Encoding of Program Semantics

International audienceIn systems with hard real-time constraints, it is necessary to compute upper bounds on the worst-case execution time (WCET) of programs; the closer the bound to the real WCET, the better. This is especially the case of synchronous reactive control loops with a fixed clock; the WCET of the loop body must not exceed the clock period. We compute the WCET (or at least a close upper bound thereof) as the solution of an optimization modulo theory problem that takes into account the semantics of the program, in contrast to other methods that compute the longest path whether or not it is feasible according to these semantics. Optimization modulo theory extends satisfiability modulo theory (SMT) to maximization problems. Immediate encodings of WCET problems into SMT yield formulas intractable for all current production-grade solvers; this is inherent to the DPLL(T) approach to SMT implemented in these solvers. By conjoining some appropriate "cuts" to these formulas, we considerably reduce the computation time of the SMT-solver. We experimented our approach on a variety of control programs, using the OTAWA analyzer both as baseline and as underlying microarchitectural analysis for our analysis, and show notable improvement on the WCET bound on a variety of benchmarks and control programs