Free Energy Wells and Overlap Gap Property in Sparse PCA

We study a variant of the sparse PCA (principal component analysis) problem in the “hard” regime, where the inference task is possible yet no polynomial-time algorithm is known to exist. Prior work, based on the low-degree likelihood ratio, has conjectured a precise expression for the best possible (subexponential) runtime throughout the hard regime. Following instead a statistical physics-inspired point of view, we show bounds on the depth of free energy wells for various Gibbs measures naturally associated to the problem. These free energy wells imply hitting time lower bounds that corroborate the low-degree conjecture: we show that a class of natural MCMC (Markov chain Monte Carlo) methods (with worst-case initialization) cannot solve sparse PCA with less than the conjectured runtime. These lower bounds apply to a wide range of values for two tuning parameters: temperature and sparsity misparametrization. Finally, we prove that the overlap gap property (OGP), a structural property that implies failure of certain local search algorithms, holds in a significant part of the hard regime. © 2022 Wiley Periodicals, Inc.     

Renner-Teller and spin-orbit vibronic coupling effects in linear triatomic molecules with a half-filled pi shell

The vibronic and spin-orbit-induced interactions among the (3)Sigma(-), (1)Delta, and (1)Sigma(+) electronic states arising from a half-filled pi orbital of a linear triatomic molecule are considered, employing the microscopic (Breit-Pauli) spin-orbit coupling operator. The 6 x 6 Hamiltonian matrix is derived in a diabatic spin-orbital electronic basis set, including terms up to fourth order in the expansion of the molecular Hamiltonian in the bending normal coordinate about the linear geometry. The symmetry properties of the Hamiltonian are analyzed. Aside from the nonrelativistic fourth-order Renner-Teller vibronic coupling within the (1)Delta state and the second-order nonrelativistic vibronic coupling between the (1)Sigma(+) and (1)Delta states, there exist zeroth-order, first-order, as well as third-order vibronic coupling terms of spin-orbit origin. The latter are absent when the phenomenological expression for the spin-orbit coupling operator is used instead of the microscopic form. The effects of the nonrelativistic and spin-orbit-induced vibronic coupling mechanisms on the (3)Sigma(-), (1)Delta, and (1)Sigma(+) adiabatic potential energy surfaces as well as on the spin-vibronic energy levels are discussed for selected parameter values.     

Ethiopian Medicinal Plants Traditionally Used for the Treatment of Cancer; Part 3: Selective Cytotoxic Activity of 22 Plants against Human Cancer Cell Lines

Medicinal plants have been traditionally used to treat cancer in Ethiopia. However, very few studies have reported the in vitro anticancer activities of medicinal plants that are collected from different agro-ecological zones of Ethiopia. Hence, the main aim of this study was to screen the cytotoxic activities of 80% methanol extracts of 22 plants against human peripheral blood mononuclear cells (PBMCs), as well as human breast (MCF-7), lung (A427), bladder (RT-4), and cervical (SiSo) cancer cell lines. Active extracts were further screened against human large cell lung carcinoma (LCLC-103H), pancreatic cancer (DAN-G), ovarian cancer (A2780), and squamous cell carcinoma of the esophagus (KYSE-70) by using the crystal violet cell proliferation assay, while the vitality of the acute myeloid leukemia (HL-60) and histiocytic lymphoma (U-937) cell lines was monitored in the 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl-2H-tetrazolium bromide (MTT) microtiter assay. Euphorbia schimperiana, Acokanthera schimperi, Kniphofia foliosa, and Kalanchoe petitiana exhibited potent antiproliferative activity against A427, RT-4, MCF-7, and SiSo cell lines, with IC₅₀ values ranging from 1.85 ± 0.44 to 17.8 ± 2.31 µg/mL. Furthermore, these four extracts also showed potent antiproliferative activities against LCLC-103H, DAN-G, A2780, KYSE-70, HL-60, and U-937 cell lines, with IC₅₀ values ranging from 0.086 to 27.06 ± 10.8 µg/mL. Hence, further studies focusing on bio-assay-guided isolation and structural elucidation of active cytotoxic compounds from these plants are warranted.     

Evaluation of solid-phase microextraction desorption parameters for fast GC analysis of cocaine in coca leaves

By its simplicity and rapidity, solid-phase microextraction (SPME) appears as an interesting alternative for sample introduction in fast gas chromatography (fast GC). This combination depends on numerous parameters affecting the desorption step (i.e., the release of compounds from the SPME fiber coating to the GC column). In this study, different liner diameters, injection temperatures, and gas flow rates are evaluated to accelerate the thermal desorption process in the injection port. This process is followed with real-time direct coupling a split/splitless injector to a mass spectrometer by means of a short capillary. It is shown that an effective, quantitative, and rapid transfer of cocaine (COC) and cocaethylene (CE) is performed with a 0.75-mm i.d. liner, at 280 degrees C and 4 mL/min gas flow rate. The 7-microm polydimethylsiloxane (PDMS) coating is selected for combination with fast GC because the 100-microm PDMS fiber presents some limitations caused by fiber bleeding. Finally, the developed SPME-fast GC method is applied to perform in less than 5 min, the quantitation of COC extracted from coca leaves by focused microwave-assisted extraction. An amount of 7.6 +/- 0.5 mg of COC per gram of dry mass is found, which is in good agreement with previously published results.     

Noncovalent Interactions of π Systems with Sulfur: The Atomic Chameleon of Molecular Recognition

The relative strength of noncovalent interactions between a thioether sulfur atom and various π systems in designed top pan molecular balances was determined by NMR spectroscopy. Compared to its oxygen counterpart, the sulfur atom displays a remarkable ability to interact with almost equal facility over the entire range of π systems studied, with the simple alkene emerging as the most powerful partner. With the exception of the O???heteroarene interaction, all noncovalent interactions of sulfur with π systems are favoured over oxygen.     

New Results on D‐Optimal Matrices

We construct a number of new supplementary difference sets (SDS) with v odd and . In particular, these give rise to D‐optimal matrices of the four new orders 206, 242, 262, 482, constructed here for the first time.     

On the compact-open and admissible topologies

It is known (see, for example, [H. Render, Nonstandard topology on function spaces with applications to hyperspaces, Trans. Amer. Math. Soc. 336 (1) (1993) 101-119; M. Escardo, J. Lawson, A. Simpson, Comparing cartesian closed categories of (core) compactly generated spaces, Topology Appl. 143 (2004) 105-145; D.N. Georgiou, S.D. Iliadis, F. Mynard, Function space topologies, in: Open Problems in Topology 2, Elsevier, 2007, pp. 15-23]) that the intersection of all admissible topologies on the set C(Y,Z) of all continuous maps of an arbitrary space Y into an arbitrary space Z, is always the greatest splitting topology (which in general is not admissible). The following, interesting in our opinion, problem is arised: when a given splitting topology (for example, the compact-open topology, the Isbell topology, and the greatest splitting topology) is the intersection of k admissible topologies, where k is a finite number. Of course, in this case this splitting topology will be the greatest splitting.In the case, where a given splitting topology is admissible the above number k is equal to one. For example, if Y is a locally compact Hausdorff space, then k=1 for the compact-open topology (see [R.H. Fox, On topologies for function spaces, Bull. Amer. Math. Soc. 51 (1945) 429-432; R. Arens, A topology for spaces of transformations, Ann. of Math. 47 (1946) 480-495; R. Arens, J. Dugundji, Topologies for function spaces, Pacific J. Math. 1 (1951) 5-31]). Also, if Y is a corecompact space, then k=1 for the Isbell topology (see [P. Lambrinos, B.K. Papadopoulos, The (strong) Isbell topology and (weakly) continuous lattices, in: Continuous Lattices and Applications, in: Lect. Notes Pure Appl. Math., vol. 101, Marcel Dekker, New York, 1984, pp. 191-211; F. Schwarz, S. Weck, Scott topology, Isbell topology, and continuous convergence, in: Lect. Notes Pure Appl. Math., vol. 101, Marcel Dekker, New York, 1984, pp. 251-271]).In [R. Arens, J. Dugundji, Topologies for function spaces, Pacific J. Math. 1 (1951) 5-31] a non-locally compact completely regular space Y is constructed such that the compact-open topology on C(Y,S), where S is the Sierpinski space, coincides with the greatest splitting topology (which is not admissible). This fact is proved by the construction of two admissible topologies on C(Y,S) whose intersection is the compact-open topology, that is k=2.In the present paper improving the method of [R. Arens, J. Dugundji, Topologies for function spaces, Pacific J. Math. 1 (1951) 5-31] we construct some other non-locally compact spaces Y such that the compact-open topology on C(Y,S) is the intersection of two admissible topologies. Also, we give some concrete problems concerning the above arised general problem.     

Lifetime of the 6793-keV state in 15O

The energy derived from the CN cycle at low stellar temperatures is regulated by the 14N(p,gamma)15O reaction. A previous direct measurement of this reaction has been interpreted as showing evidence for a subthreshold resonance which makes a major contribution to the reaction rate at low temperatures. This resonance, at E(c.m.) = -504 keV would correspond to the known Ex = 6793-keV state in 15O. We have measured a mean lifetime of 1.60(+0.75)(-0.72) fs (90% C.L.) for this state using the Doppler-shift attenuation method. This lifetime is a factor of 15 longer than that inferred from the (p,gamma) data and implies that the contribution of the subthreshold resonance is negligible.     

Microphase separation of cationic poly(N-isopropylacrylamide) copolymers in water: Effect of the migration of charges

The structures of aqueous copolymer solutions have been examined through small angle neutron scattering. The copolymers contained mostly N-isopropylacrylamide (NIPAM) monomers. Poly (NIPAM) solutions have a lower critical solution temperature (LCST), above which the macromolecules separate from water. A small fraction of ionizable N,N-[(dimethylamino) propyl] methacrylamide (MADAP) monomers was introduced into the macromolecules. This had dramatic consequences on the solution behavior at temperatures above the LCST of PNIPAM, where phase separation would have been expected for the homopolymer. When all MADAP monomers were ionized, it was found that the solutions resisted the phase separation. At short spatial scales, the chains were collapsed but at large scales they formed branched aggregates that did not separate out of water. When only half of the MADAP monomers are ionized, the electrical charges were able to redistribute themselves along the chains. In this case, the rise in temperature caused a microphase separation where the electrical charges were relocated on a fraction of the chains that remained in solution.The other chains (or section of chains) formed large nodules of a polymer rich phase.     

Inelastic incoherent neutron scattering measurements of intact cells and tissues and detection of interfacial water

We have previously used inelastic incoherent neutron scattering spectroscopy to investigate the properties of aqueous suspensions of biomolecules as a function of hydration. These experiments led to the identification of signals corresponding to interfacial (hydration) water at low water content. A prediction from these studies was that in the crowded environment inside living cells, a significant proportion of the water would be interfacial, with profound implications for biological function. Here we describe the first inelastic incoherent neutron scattering spectroscopy studies of living cells and tissues. We find that the interfacial water signal is similar to that observed for water interacting with purified biomolecules and other solutes, i.e., it is strongly perturbed in the librational and translational intermolecular optical regions of the spectrum at 20-150 meV. The ratio of interfacial water compared to total water in cells (approximately 30%) is in line with previous experimental data for hydration water and calculations based on simple assumptions.