We consider the problem of signal estimation (denoising) from a statistical-mechanical perspective, in continuation to a recent work on the analysis of mean-square error (MSE) estimation using a direct relationship between optimum estimation and certain partition functions. The paper consists of essentially two parts. In the first part, using the aforementioned relationship, we derive single-le...

We describe an approach to the study of phase transitions in Potts models based on an estimate of the complexity of the locus of real zeros of the partition function, computed in terms of the classes in the Grothendieck ring of the affine algebraic varieties defined by the vanishing of the multivariate Tutte polynomial. We give completely explicit calculations for the examples of the chains of ...

The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by studying the three-dimensional hard-sphere model. Having obtained the partition function, we show how easy it is to calculate the compressibility and the free...

Aqueous Two Phase System (ATPS) or liquid-liquid extraction is used in biotechnology to recover valuable compounds from raw sources. In Two-Phase Systems, many factors influence the Partition coefficient, K, (which ratio of protein concentration top phase that bottom phase) and Recovery percentage (Rec%). this research, two systems ATPS were used: first, polyethylene glycol (PEG) 4000/Sodium ci...

We consider the problem of partitioning n integers into two subsets of given cardinalities such that the discrepancy, the absolute value of the difference of their sums, is minimized. The integers are i.i.d. random variables chosen uniformly from the set {1, . . . , M}. We study how the typical behavior of the optimal partition depends on n, M and the bias s, the difference between the cardinal...

We study the problem of approximately evaluating the independent set polynomial of boundeddegree graphs at a point λ. Equivalently, this problem can be reformulated as the problem of approximating the partition function of the hard-core model with activity λ on graphs G of maximum degree ∆. For λ > 0, breakthrough results of Weitz and Sly established a computational transition from easy to hard...

Earth’s core may contain C, and it has been suggested that C in the core could stabilize the formation of a solid inner core composed of Fe3C. We experimentally examined the Fe–C system at a pressure of 5 GPa and determined the Fe–C phase diagram at this pressure. In addition, we measured solid metal/liquid metal partition coefficients for 17 trace elements and examined the partitioning behavio...

The partition ratios of radioactive fatty acids between n-heptane and a physiological buffer at 37 degrees C were measured. The fatty acids included the saturated acids with an even number of carbons from 10 to 18 and the unsaturated acids oleic, linoleic, and linolenic. In addition, the partition ratios of decanoate, myristate, and palmitate were determined over a wide pH range. Any single plo...

The paper deals with design of PID controller for unstable SISO systems in the frequency domain. The method is accomplished with performance specification in terms of phase margin and the modification of Neimark D-partition method which ensures desired phase margin. The practical application is illustrated by the PID controller design for the Magnetic Levitation Model.