Formal Verification of Nonlinear Inequalities with Taylor Interval Approximations

We present a formal tool for verification of multivariate nonlinear inequalities. Our verification method is based on interval arithmetic with Taylor approximations. Our tool is implemented in the HOL Light proof assistant and it is capable to verify multivariate nonlinear polynomial and non-polynomial inequalities on rectangular domains. One of the main features of our work is an efficient implementation of the verification procedure which can prove non-trivial high-dimensional inequalities in several seconds. We developed the verification tool as a part of the Flyspeck project (a formal proof of the Kepler conjecture). The Flyspeck project includes about 1000 nonlinear inequalities. We successfully tested our method on more than 100 Flyspeck inequalities and estimated that the formal verification procedure is about 3000 times slower than an informal verification method implemented in C++. We also describe future work and prospective optimizations for our method.Comment: 15 page

Insulin and Glucagon Impairments in Relation with Islet Cells Morphological Modifications Following Long Term Pancreatic Duct Ligation in the Rabbit – A Model of Non-insulin-dependent Diabete

Plasma levels of glucose, insulin and glucagon were measured at various time intervals after pancreatic duct ligation (PDL) in rabbits. Two hyperglycemic periods were observed: one between 15–90 days (peak at 30 days of 15.1 ± 1.2mmol/l, p < 0.01), and the other at 450 days (11.2 ± 0.5 mmol/l, p < 0.02). The first hyperglycemic episode was significantly correlated with both hypoinsulinemia (41.8 ± 8pmol/l, r= –0.94, p < 0.01) and hyperglucagonemia (232 ± 21ng/l, r=0.95, p < 0.01). However, the late hyperglycemic phase (450 days), which was not accompanied by hypoinsulinemia, was observed after the hyperglucagonemia (390 days) produced by abundant immunostained A-cells giving rise to a 3-fold increase in pancreatic glucagon stores. The insulin and glucagon responses to glucose loading at 180, 270 and 450 days reflected the insensitivity of B- and A-cells to glucose. The PDL rabbit model with chronic and severe glycemic disorders due to the predominant role of glucagon mimicked key features of the NIDDM syndrome secondary to exocrine disease

Acute hormonal response to glucose, lipids and arginine infusion in overweight cats

In cats, the incidence of obesity and diabetes is increasing, and little is known about specific aspects of the endocrine control of food intake in this species. Recent data suggest that ghrelin has an important role in the control of insulin secretion and vice versa, but this role has never been demonstrated in cats. Here we aimed to improve our understanding about the relationship between insulin, amylin and ghrelin secretion in response to a nutrient load in overweight cats. After a 16h fast, weekly, six overweight male cats underwent randomly one of the four testing sessions: saline, glucose, arginine and TAG. All solutions were isoenergetic and isovolumic, and were injected intravenously as a bolus. Glucose, insulin, acylated ghrelin (AG), amylin and prolactin were assayed in plasma before and 10, 20, 40, 60, 80 and 100min after the nutrient load. A linear mixed-effects model was used to assess the effect of bolus and time on the parameters. A parenteral bolus of glucose or arginine increased insulin and ghrelin concentrations in cats. Except for with the TAG bolus, no suppression of ghrelin was observed. The absence of AG suppression after the intravenous load of arginine and glucose may suggest: (1) that some nutrients do not promote satiation in overweight cats; or that (2) AG may be involved in non-homeostatic consumption mechanisms. However, the role of ghrelin in food reward remains to be assessed in cat

The Kinase Function of MSK1 Regulates BDNF Signaling to CREB and Basal Synaptic Transmission, But Is Not Required for Hippocampal Long-Term Potentiation or Spatial Memory

The later stages of long-term potentiation (LTP) in vitro and spatial memory in vivo are believed to depend upon gene transcription. Accordingly, considerable attempts have been made to identify both the mechanisms by which transcription is regulated and indeed the gene products themselves. Previous studies have shown that deletion of one regulator of transcription, the mitogen- and stress-activated kinase 1 (MSK1), causes an impairment of spatial memory. Given the ability of MSK1 to regulate gene expression via the phosphorylation of cAMP response element binding protein (CREB) at serine 133 (S133), MSK1 is a plausible candidate as a prime regulator of transcription underpinning synaptic plasticity and learning and memory. Indeed, prior work has revealed the necessity for MSK1 in homeostatic and experience-dependent synaptic plasticity. However, using a knock-in kinase-dead mouse mutant of MSK1, the current study demonstrates that, while the kinase function of MSK1 is important in regulating the phosphorylation of CREB at S133 and basal synaptic transmission in hippocampal area CA1, it is not required for metabotropic glutamate receptor-dependent long-term depression (mGluR-LTD), two forms of LTP or several forms of spatial learning in the watermaze. These data indicate that other functions of MSK1, such as a structural role for the whole enzyme, may explain previous observations of a role for MSK1 in learning and memory

Automatic Verification of Finite Precision Implementations of Linear Controllers

We consider the problem of verifying finite precision implementation of linear time-invariant controllers against mathematical specifications. A specification may have multiple correct implementations which are different from each other in controller state representation, but equivalent from a perspective of input-output behavior (e.g., due to optimization in a code generator). The implementations may use finite precision computations (e.g. floating-point arithmetic) which cause quantization (i.e., roundoff) errors. To address these challenges, we first extract a controller\u27s mathematical model from the implementation via symbolic execution and floating-point error analysis, and then check approximate input-output equivalence between the extracted model and the specification by similarity checking. We show how to automatically verify the correctness of floating-point controller implementation in C language using the combination of techniques such as symbolic execution and convex optimization problem solving. We demonstrate the scalability of our approach through evaluation with randomly generated controller specifications of realistic size

Automatic Estimation of Verified Floating-Point Round-Off Errors via Static Analysis

This paper introduces a static analysis technique for computing formally verified round-off error bounds of floating-point functional expressions. The technique is based on a denotational semantics that computes a symbolic estimation of floating-point round-o errors along with a proof certificate that ensures its correctness. The symbolic estimation can be evaluated on concrete inputs using rigorous enclosure methods to produce formally verified numerical error bounds. The proposed technique is implemented in the prototype research tool PRECiSA (Program Round-o Error Certifier via Static Analysis) and used in the verification of floating-point programs of interest to NASA

Influences of Excluded Volume of Molecules on Signaling Processes on Biomembrane

We investigate the influences of the excluded volume of molecules on biochemical reaction processes on 2-dimensional surfaces using a model of signal transduction processes on biomembranes. We perform simulations of the 2-dimensional cell-based model, which describes the reactions and diffusion of the receptors, signaling proteins, target proteins, and crowders on the cell membrane. The signaling proteins are activated by receptors, and these activated signaling proteins activate target proteins that bind autonomously from the cytoplasm to the membrane, and unbind from the membrane if activated. If the target proteins bind frequently, the volume fraction of molecules on the membrane becomes so large that the excluded volume of the molecules for the reaction and diffusion dynamics cannot be negligible. We find that such excluded volume effects of the molecules induce non-trivial variations of the signal flow, defined as the activation frequency of target proteins, as follows. With an increase in the binding rate of target proteins, the signal flow varies by i) monotonically increasing; ii) increasing then decreasing in a bell-shaped curve; or iii) increasing, decreasing, then increasing in an S-shaped curve. We further demonstrate that the excluded volume of molecules influences the hierarchical molecular distributions throughout the reaction processes. In particular, when the system exhibits a large signal flow, the signaling proteins tend to surround the receptors to form receptor-signaling protein clusters, and the target proteins tend to become distributed around such clusters. To explain these phenomena, we analyze the stochastic model of the local motions of molecules around the receptor.Comment: 31 pages, 10 figure

Polynomial function intervals for floating-point software verification

The focus of our work is the verification of tight functional properties of numerical programs, such as showing that a floating-point implementation of Riemann integration computes a close approximation of the exact integral. Programmers and engineers writing such programs will benefit from verification tools that support an expressive specification language and that are highly automated. Our work provides a new method for verification of numerical software, supporting a substantially more expressive language for specifications than other publicly available automated tools. The additional expressivity in the specification language is provided by two constructs. First, the specification can feature inclusions between interval arithmetic expressions. Second, the integral operator from classical analysis can be used in the specifications, where the integration bounds can be arbitrary expressions over real variables. To support our claim of expressivity, we outline the verification of four example programs, including the integration example mentioned earlier. A key component of our method is an algorithm for proving numerical theorems. This algorithm is based on automatic polynomial approximation of non-linear real and real-interval functions defined by expressions. The PolyPaver tool is our implementation of the algorithm and its source code is publicly available. In this paper we report on experiments using PolyPaver that indicate that the additional expressivity does not come at a performance cost when comparing with other publicly available state-of-the-art provers. We also include a scalability study that explores the limits of PolyPaver in proving tight functional specifications of progressively larger randomly generated programs

Molecular imaging of glioblastoma multiforme using anti-insulin-like growth factor-binding protein-7 single-domain antibodies

BACKGROUND: Insulin-like growth factor-binding protein 7 (IGFBP7) is an abundant, selective and accessible biomarker of glioblastoma multiforme (GBM) tumour vessels. In this study, an anti-IGFBP7 single-domain antibody (sdAb) was developed to target GBM vessels for molecular imaging applications. METHODS: Human GBM was modelled in mice by intracranial implantation of U87MG.EGFRvIII cells. An anti-IGFBP7 sdAb, isolated from an immune llama library by panning, was assessed in vitro for its binding affinity using surface plasmon resonance and by ex vivo immunobinding on mouse and human GBM tissue. Tumour targeting by Cy5.5-labelled anti-IGFBP7 sdAb as well as by anti-IGFBP7 sdAb conjugated to PEGylated Fe3O4 nanoparticles (NPs)-Cy5.5 were assessed in U87MG.EGFRvIII tumour-bearing mice in vivo using optical imaging and in brain sections using fluorescent microscopy. RESULTS: Surface plasmon resonance analyses revealed a medium affinity (KD\ufffd40\ufffd50 nM) binding of the anti-IGFBP7 sdAb to the purified antigen. The anti-IGFBP7 sdAb also selectively bound to both mouse and human GBM vessels, but not normal brain vessels in tissue sections. In vivo, intravenously injected anti-IGFBP7 sdAb-Cy5.5 bound to GBM vessels creating high imaging signal in the intracranial tumour. Similarly, the anti-IGFBP7 sdAb-functionalised PEGylated Fe3O4 NP-Cy5.5 demonstrated enhanced tumour signal compared with non-targeted NPs. Fluorescent microscopy confirmed the presence of anti-IGFBP7 sdAb and anti-IGFBP7 sdAb- PEGylated Fe3O4 NPs selectively in GBM vessels. CONCLUSIONS: Anti-IGFBP7 sdAbs are novel GBM vessel-targeting moieties suitable for molecular imaging.Peer reviewed: YesNRC publication: Ye

Acute tubulointerstitial nephritis complicating Legionnaires' disease: a case report

<p>Abstract</p> <p>Introduction</p> <p>Legionnaires' disease is recognized as a multi-systemic illness. Afflicted patients may have pulmonary, renal, gastrointestinal tract and central nervous system complications. However, renal insufficiency is uncommon. The spectrum of renal involvement may range from a mild and transient elevation of serum creatinine levels to anuric renal failure requiring dialysis and may be linked to several causes. In our present case report, we would like to draw attention to the importance of the pathological documentation of acute renal failure by reporting a case of a patient with acute tubulointerstitial nephritis complicating Legionnaires' disease.</p> <p>Case presentation</p> <p>A 55-year-old Caucasian man was admitted to our hospital for community-acquired pneumonia complicated by acute renal failure. <it>Legionella pneumophila </it>serogroup type 1 was diagnosed. Although the patient's respiratory illness responded to intravenous erythromycin and ofloxacin therapy, his renal failure worsened, he became anuric, and hemodialysis was started. A renal biopsy was performed, which revealed severe tubulointerstitial nephritis. After initiation of steroid therapy, his renal function improved dramatically.</p> <p>Conclusions</p> <p>This case highlights the importance of kidney biopsies in cases where acute renal failure is a complicating factor in Legionnaires' disease. If the presence of acute tubulointerstitial nephritis can be confirmed, it will likely respond favorably to steroidal treatment and thus irreversible renal damage and chronic renal failure will be avoided.</p