Bayesian generalized probability calculus for density matrices

One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be diagonal. We develop a probability calculus based on these more general distributions that includes definitions of joints, conditionals and formulas that relate these, including analogs of the Theorem of Total Probability and various Bayes rules for the calculation of posterior density matrices. The resulting calculus parallels the familiar “conventional” probability calculus and always retains the latter as a special case when all matrices are diagonal. We motivate both the conventional and the generalized Bayes rule with a minimum relative entropy principle, where the Kullbach-Leibler version gives the conventional Bayes rule and Umegaki’s quantum relative entropy the new Bayes rule for density matrices. Whereas the conventional Bayesian methods maintain uncertainty about which model has the highest data likelihood, the generalization maintains uncertainty about which unit direction has the largest variance. Surprisingly the bounds also generalize: as in the conventional setting we upper bound the negative log likelihood of the data by the negative log likelihood of the MAP estimator.     

Verification of $${{EB}^3}$$ specifications using CADP

\({{\small {EB}}^3}\) is a specification language for information systems. The core of the \({{\small {EB}}^3}\) language consists of process algebraic specifications describing the behaviour of the entities in a system, and attribute function definitions describing the entity attributes. The verification of \({{\small {EB}}^3}\) specifications against temporal properties is of great interest to users of \({{\small {EB}}^3}\). In this paper, we propose a translation from \({{\small {EB}}^3}\) to LOTOS NT (LNT for short), a value-passing concurrent language with classical process algebra features. Our translation ensures the one-to-one correspondence between states and transitions of the labelled transition systems corresponding to the \({{\small {EB}}^3}\) and LNT specifications. We automated this translation with the \({{{\small {EB}}^3}2{\small {LNT}}}\) tool, thus equipping the \({{\small {EB}}^3}\) method with the functional verification features available in the CADP toolbox.     

A lower bound for randomized algebraic decision trees

We prove the firstnontrivial (andsuperlinear) lower bounds on the depth ofrandomized algebraic decision trees (with two-sided error) for problems being finite unions of hyperplanes and intersections of halfspaces, solving a long standing open problem. As an application, among other things, we derive, for the first time, an (n ²)randomized lower bound for theKnapsack Problem, and an (n logn)randomized lower bound for theElement Distinctness Problem which were previously known only for deterministic algebraic decision trees. It is worth noting that for the languages being finite unions of hyperplanes our proof method yields also a new elementary lower bound technique for deterministic algebraic decision trees without making use of Milnor's bound on Betti number of algebraic varieties.     

A Sodium Oxalate-Rich Diet Induces Chronic Kidney Disease and Cardiac Dysfunction in Rats

Chronic kidney disease (CKD) is a worldwide public health issue affecting 14% of the general population. However, research focusing on CKD mechanisms/treatment is limited because of a lack of animal models recapitulating the disease physiopathology, including its complications. We analyzed the effects of a three-week diet rich in sodium oxalate (OXA diet) on rats and showed that, compared to controls, rats developed a stable CKD with a 60% reduction in glomerular filtration rate, elevated blood urea levels and proteinuria. Histological analyses revealed massive cortical disorganization, tubular atrophy and fibrosis. Males and females were sensitive to the OXA diet, but decreasing the diet period to one week led to GFR significance but not stable diminution. Rats treated with the OXA diet also displayed classical CKD complications such as elevated blood pressure and reduced hematocrit. Functional cardiac analyses revealed that the OXA diet triggered significant cardiac dysfunction. Altogether, our results showed the feasibility of using a convenient and non-invasive strategy to induce CKD and its classical systemic complications in rats. This model, which avoids kidney mass loss or acute toxicity, has strong potential for research into CKD mechanisms and novel therapies, which could protect and postpone the use of dialysis or transplantation.     

Serial ATA Ⅱ中S参数和确定性抖动一致性测试

SATAⅡ频域测试 SATAⅡ规范要求大量的测试，包括电缆和连接器（无源物理层）的时域测试、发射机和接收机的时域测试、电缆和连接器（无源物理层）的频域测试、发射机和接收机的频域测试等等。其中发射机和接收机的频域测试又包括：     

Algorithms for Computing Sparse Shifts for Multivariate Polynomials

In this paper, we investigate the problem of finding t-sparse shifts for multivariate polynomials. Given a polynomial f∈ℱ[x ₁, x ₂, …, x _n ] of degree d, and a positive integer t, we consider the problem of representing f(x) as a ?-linear combination of the power products of u _i where u _i = x _i −b _i for some b _i ∈?, an extension of ℱ, for i = 1, …, n, i.e., f = ∑ _j F _j u ^αj , in which at most t of the F _j are non-zero. We provide sufficient conditions for uniqueness of sparse shifts for multivariate polynomials, prove tight bounds on the degree of the polynomial being interpolated in terms of the sparsity bound t and a bound on the size of the coefficients of the polynomial in the standard representation, and describe two new efficient algorithms for computing sparse shifts for a multivariate polynomial. Received: January 30, 1996; revised version: January 15, 2000     

The effects of sodium hexametaphosphate addition on the physicochemical properties and microstructure of the milk fat globule membrane (MFGM) in liquid milk after freezing

This research examined the effects of sodium hexametaphosphate on the physicochemical properties and the microstructure of the milk fat globule membrane (MFGM) after freezing. The particle size distribution showed that the peak of the MFGM in the controlled sample was higher than the peak in the frozen sample. The MFGM sample that contained the highest concentration of sodium hexametaphosphate displayed the highest peak. The MFGM samples with the highest concentrations of sodium hexametaphosphate were more stable than the samples with the lowest concentrations. Sodium dodecyl sulfate Polyacrylamide gel electrophoresis and scanning electron microscopy showed sizeable destruction of the MFGM after freezing.     

Migration of mineral oil from party plates of recycled paperboard into foods: 1. Is recycled paperboard fit for the purpose? 2. Adequate testing procedure

Party plates made of recycled paperboard with a polyolefin film on the food contact surface (more often polypropylene than polyethylene) were tested for migration of mineral oil into various foods applying reasonable worst case conditions. The worst case was identified as a slice of fried meat placed onto the plate while hot and allowed to cool for 1 h. As it caused the acceptable daily intake (ADI) specified by the Joint FAO/WHO Expert Committee on Food Additives (JECFA) to be exceeded, it is concluded that recycled paperboard is generally acceptable for party plates only when separated from the food by a functional barrier. Migration data obtained with oil as simulant at 70°C was compared to the migration into foods. A contact time of 30 min was found to reasonably cover the worst case determined in food.