Arnol′d Diffusion in a Pendulum Lattice

The main model studied in this paper is a lattice of pendula with a nearest‐neighbor coupling. If the coupling is weak, then the system is near‐integrable and KAM tori fill most of the phase space. For all KAM trajectories the energy of each pendulum stays within a narrow band for all time. Still, we show that for an arbitrarily weak coupling of a certain localized type, the neighboring pendula can exchange energy. In fact, the energy can be transferred between the pendula in any prescribed way. © 2014 Wiley Periodicals, Inc.     

Some algebraic structures for diffusion in social networks

Restrictions on influence structures discussed by Buskens and Yamaguchi (1999) and others lead the states of possible distributions of information to form an algebraic structure of a lattice that is closed under union. From an examination of such a lattice of distribution, it is possible to recreate an influence network that is not observed directly. Finally, it is noted that these structures are different from those examined via Galois lattices; therefore, if these diffusion processes occur, Galois lattices do not recreate the actual social structure underlying this diffusion.     

Theoretical optimization of Irinotecan-based anticancer strategies in the case of drug-induced efflux

The anticancer drug Irinotecan (CPT11) is known to trigger the induction of ATP-Binding Cassette (ABC) transporters, responsible for the efflux of the drug and its metabolites outside of the cells. The drug-modulated overexpression of those transporters prevents its accumulation in the intracellular medium, therefore decreasing its efficacy. A critical clinical concern lies in the design of CPT11-based therapeutic strategies which eradicate a maximum number of cancer cells despite their ability to become resistant. In order to address this issue, we supplemented an existing mathematical model of CPT11 molecular pharmacokinetics–pharmacodynamics (PK–PD) with a new model of CPT11-induced overexpression of ABC transporters. We then theoretically optimized exposure to CPT11 given as a single agent or combined either with ABC transporter inhibitors, or with inhibitors of nuclear factors whose activation is responsible for transporter overexpression. We firstly considered a cancer cell population endowed with the ability of inducing their transporters. For any drug combination, we concluded that the highest concentration of CPT11 should be administered in order to kill a maximum number of cancer cells, despite the triggering of resistance. We then considered a population of healthy cells which were assumed to be identical to cancer cells except that they were not able to become resistant. Optimal schemes were defined as the ones which maximized DNA damage in cancer cells under the constraint of DNA damage in healthy cells not exceeding a tolerability threshold. The optimal therapeutic strategy consisted in combining CPT11 with ABC transporter inhibitors as it achieved a complete reversal of resistance by means of the lowest concentrations of CPT11.     

Inductivism and Parmenidean epistemology: Kyburg’s way

cording to Henry Kyburg, all extralogical and extramathematical propositions accepted as evidence and all propositions accepted inductively on the basis of such evidence are uncertain. There is a possibility of error. Consequently, neither the corpus of inductively accepted statements nor the corpus of statements accepted as evidence can serve as a standard for serious possibility in the sense I have deployed since the 1970s. The standard for serious possibility remains an unchanging Parmenidean standard. In contrast to other Parmenidean epistemologists that eschew inductive acceptances Kyburg insists that the corpus of evidence and of inductively accepted statements is subject to critical review and change; but the changes have no bearing on the standard for serious possibility.have always agreed with Henry’s emphasis on a distinction between acceptance as evidence and inductive acceptance. But I have insisted that the corpus of evidence or state of full belief is a standard for serious possibility and that the standard is subject to modification.burg does think of acceptance as evidence and inductive acceptance as modal notions and has recently used the expression “serious possibility” in this connection. But when Kyburg and Teng speak of “risky knowledge”, they are speaking of claims that might be false in the sense of serious possibility that they seem to be suggesting is immune to change and seems to correlate with serious possibility as I have used it since the 1970s. So acceptance (both inductive and evidential) are modal notions subject to change but are not to be confused with the notion of serious possibility of error or riskiness.     

On congruences of-normal semigroups-normal semigroups

Communicated by G. Lallement     

Experimental determination of rheological properties of polydimethylsiloxane

A series of linear polydimethylsiloxane of different molecular weight and with reduced polydispersity were prepared by partial fractionation of commercial products. The rheological functions, i.e. zero shear viscosity (η₀), first and second normal stress coefficients (Ψ₁₀ and Ψ₂₀), of the materials were experimentally measured by conventional rotational rheometers and by a rotation rod apparatus. The relationships between molecular structure (molecular weight and polydispersity index) and rheological functions are presented and discussed on the basis of equations proposed in the literature. Zero shear viscosity data conform to the well-known dependence on a power 3.5 of molecular weight. However, a consistently stronger influence of molecular weight over Ψ₁₀ and Ψ₂₀ is found. The influence of polydispersity over Ψ₁₀ is also analyzed.     

Nilpotent Ranks of Semigroups of Partial Transformations

A subset U of a semigroup S is a generating set for S if every element of S may be written as a finite product of elements of U. The rank of a finite semigroup S is the size of a minimal generating set of S, and the nilpotent rank of S is the size of a minimal generating set of S consisting of nilpotents in S. A partition of a q-element subset of the set X_n = {1,2,..., n} is said to be of type τ if the sizes of its classes form the partition τ of the positive integer q ≤ n. A non-trivial partition τ of q consists of k < q elements. For a non-trivial partition τ of q < n, the semigroup S(τ), generated by all the transformations with kernels of type τ, is nilpotent-generated. We prove that if τ is a non-trivial partition of q < n, then the rank and the nilpotent rank of S(τ) are both equal to the number of partitions X_n of type τ.     

A Direct Construction of Nontransitive Dice Sets

In this paper, we give a direct construction for a set of dice realizing any given tournament T. The construction for a tournament with n vertices requires dice with n sides if n is odd, sides if n is divisible by 4, and sides if mod 4. This appears to be the most efficient general construction to date. Our construction relies only on a standard construction from graph theory.