Generic Expression Hardness Results for Primitive Positive Formula Comparison

We study the expression complexity of two basic problems involving the comparison of primitive positive formulas: equivalence and containment. In particular, we study the complexity of these problems relative to finite relational structures. We present two generic hardness results for the studied problems, and discuss evidence that they are optimal and yield, for each of the problems, a complexity trichotomy

Synthesis and Biological Evaluation of Novel N-phenyl-5-carboxamidyl Isoxazoles as Potential Chemotherapeutic Agents for Colon Cancer

Abstract A new series of isoxazole derivatives, N-phenyl-5-carboxamidyl isoxazoles, was investigated for their anticancer activity with solid tumor selectivity. Six N-phenyl-5-carboxamidylisoxazoles were chemically synthesized and evaluated by the in vitro disk-diffusion assay and IC 50 cytotoxicity determination. The results showed that one of the derivatives, compound 3, N-(4-chlorophenyl)-5-carboxamidyl isoxazole, was the most active against colon 38 and CT-26 mouse colon tumor cells with an IC 50 of 2.5 µg/mL for both cell lines. Western blot analysis showed that compound 3 significantly down-regulated the expression of phosphorylated STAT3 in both human and mouse colon cancer cells indicating that the mechanism of action for compound 3 may involve the inhibition of JAK3/STAT3 signaling pathways. Flow cytometric analysis with Annexin V staining showed that the death induced by compound 3 is mediated through cell necrosis and not apoptotic pathway. In summary, our results show that compound 3 is a new N-phenyl-5-carboxamidyl isoxazole with potential anticancer activity. Compound 3 inhibits the phosphorylation of STAT3, a novel target for chemotherapeutic drugs, and is worthy of further investigation as a potential chemotherapeutic agent for treating colon cancer

On solvable congruences in finitely decidable varieties

In this paper we establish the (1, 2) and (2, 1)-transfer principles for finitely decidable locally finite varieties. A class of structures is finitely decidable if the first order theory of its finite members is recursive. A variety is a class of algebras which is axiomatizable by a set of equations. The transfer principles deal with the local structure of finite algebras and have strong global consequences.

Some properties of finitely decidable varieties

Abstract: "Let V be a variety whose class of finite members has a decidable first-order theory. We prove that each finite member A of V satisfies the (3,1) and (3,2) transfer principles, and that the minimal sets of prime quotients of type 2 or 3 in A must have empty tails. The first result has already been used by J. Jeong [9] in characterizing the finite subdirectly irreducible members of V with nonabelian monolith. The second result implies that if V is also locally finite and omits type 1, then V is congruence modular.

Lectures on algebraic model theory

In recent years, model theory has had remarkable success in solving important problems as well as in shedding new light on our understanding of them. The three lectures collected here present recent developments in three such areas: Anand Pillay on differential fields, Patrick Speissegger on o-minimality and Matthias Clasen and Matthew Valeriote on tame congruence theory