On the universal Gröbner bases of toric ideals of graphs

The universal Gröbner basis of an ideal is a Gröbner basis with respect to all term orders simultaneously. We characterize in graph theoretical terms the elements of the universal Gröbner basis of the toric ideal of a graph. We also provide a new degree bound. Finally, we give examples of graphs for which the true degrees of their circuits are less than the degrees of some elements of the Graver basis.     

The Chen-Type of the Spiral Surfaces

We show that a spiral surface M in E³ is of finite type if and only if M is minimal Also, the plane is the only spiral surface in E³ whose the Gauss map G is of finite type, or satisfies the condition ΔG = ΛG, where Λ ∈ R^3×3.     

Tumor Hypoxia Heterogeneity Affects Radiotherapy: Inverse-Percolation Shell-Model Monte Carlo Simulations

Tumor hypoxia was discovered a century ago, and the interference of hypoxia with all radiotherapies is well known. Here, we demonstrate the potentially extreme effects of hypoxia heterogeneity on radiotherapy and combination radiochemotherapy. We observe that there is a decrease in hypoxia from tumor periphery to tumor center, due to oxygen diffusion, resulting in a gradient of radiative cell-kill probability, mathematically expressed as a probability gradient of occupied space removal. The radiotherapy-induced break-up of the tumor/TME network is modeled by the physics model of inverse percolation in a shell-like medium, using Monte Carlo simulations. The different shells now have different probabilities of space removal, spanning from higher probability in the periphery to lower probability in the center of the tumor. Mathematical results regarding the variability of the critical percolation concentration show an increase in the critical threshold with the applied increase in the probability of space removal. Such an observation will have an important medical implication: a much larger than expected radiation dose is needed for a tumor breakup enabling successful follow-up chemotherapy. Information on the TME’s hypoxia heterogeneity, as shown here with the numerical percolation model, may enable personalized precision radiation oncology therapy.     

A convenient MnIII starting material for the synthesis of homo- and heterometallic manganese carboxylate clusters: Mn9 and Mn10−xFex complexes

The use of a convenient source of Mn^III ions, namely the [Mn(OR)(O₂CR′)₂]_n (R = H, Me, and R′ = Me, Bu^t) family of 1-D coordination polymers, afforded two new enneanuclear and decanuclear molecular clusters, homometallic [Mn₉O₇(O₂CBu^t)₁₃(MeCN)₂] (3) and heterometallic [Mn_10?xFe_x(OMe)₂₀(O₂CMe)₁₀] (x < 10) (4), respectively. Compound 3 was synthesized by a solvent-induced structural transformation, whereas complex 4 resulted from the reaction of [Mn(OH)(O₂CMe)₂]_n with an Fe^III source. The core of 3 comprises two [Mn₄O₂]⁸⁺ butterfly units and a [Mn₃O]⁷⁺ triangular unit fused together by sharing one Mn atom. Magnetic susceptibility measurements of 3 revealed dominant antiferromagnetic interactions within the molecule, and a ground state of S = 1 with many low-lying excited states. Complex 4 is a mixed Fe^III/Mn^III single-strand molecular wheel, which forms 3D nanotubular stacks arranged in a zig–zag fashion. The described work suggests that the [Mn(OR)(O₂CR′)₂]_n compounds represent excellent starting materials for Mn^III carboxylate cluster chemistry.     

Symbolic space determinations on physical limitations

In the quest for the determination of the physical limitations imposed on computing (Bledsoe, 1961; Bremermann, 1962; Ligomenides, 1967, 1968; Keyes and Landauer, 1970; Keyes, 1975), unless we introduce basic considerations relating to such things as the computing philosophy and methodology employed, the encoding and translation languages, and techniques, and the question of computability and intractability, our investigation limits itself to pursuit of outer bounds on energy, time, and spacing requirements for the transfer storage and processing of two-state signal quanta, rather than dealing with bounds on processing information which is specially encoded for computation. It seems that limitations imposed in the symbolic space precede by several orders of magnitude those in the energy space.     

The bounded-open topology on function spaces

For any regular space Z It is shown, 1) that the bounded-open topology T on C(Y,Z) is splitting and it is also the smallest jointly continuous topology whenever Y is locally bounded, 2) if Y is locally bounded or if X × Y is a boundedly generated space, then there is a natural bijection on C(X × Y,Z) onto C(X,(C(Y,Z),T_eo) which is actually a homeomorphism with respect to the bounded-open topology on both function spaces, 3) The path components of (C(Y,Z),T_eo) are exactly its homotopy classes whenever Y is boundedly generated, 4) The bounded-open topology Teo induces contravariant and covariant Homotopy preserving function-space functors. Further, 5) T_eo reduces to the compact-open topology t_co whenever the domain Y is regular; but in general, T_eo is finer than T_co (assuming the domain is Hausdorff or the range is either Hausdorff or regular).     

Stereology versus planimetry to estimate the volume of malignant liver lesions on MR imaging

Liver tumor volume measurements are clinically useful in patients undergoing cancer treatment. The techniques of planimetry and stereology were applied for this purpose on magnetic resonance (MR) imaging. Fifty-eight malignant liver lesions were depicted on MR images in 20 consecutive patients. The volume of all lesions was estimated using stereology technique, based on point counting. Stereological tumor volume estimations were compared with those determined by manual planimetry. The repeatability of both techniques was assessed. Tumor volumes estimated by the two techniques were highly correlated (r = 0.98, p < 0.0001). The 95% limits of agreement showed that the stereological volume estimations may differ from the planimetric assessments by less than 23%. Both techniques presented comparable intra- and interobserver variability. The planimetry was 1.5 times faster than the stereology. Both volumetric techniques may provide reliable and reproducible liver tumor volume estimations. The planimetry may be the method of choice because of its superior speed.     

Self-induced transparency in diblock copolymer dispersions

We report on the versatile effect of weak red laser light impinging on diblock copolymer [poly(isoprene-b-styrene)] dispersions in two selective solvents for each block. In the strongly scattering but transparent micellar solutions in hexane (a good solvent for polyisoprene), higher refractive index copolymer-rich fibers were formed. In the turbid dispersions of the same copolymer in ethyl acetate (a good solvent for polystyrene), the effect of self-induced transparency was observed. A two-step patterning mechanism caused the generation of a transparent microchannel, increasing light transmission. The analogy between the current effect and that observed in homopolymer polyisoprene solutions in different solvents is discussed toward an understanding of the unanticipated light-soft-matter interaction.     

Changes of gross gamma-ray intensity in a submarine spring system due to a distant earthquake event on 30th of March 2019 at Itea,Greece

Journal of Radioanalytical and Nuclear Chemistry - A medium resolution underwater in-situ gamma-ray spectrometer (GeoMAREA) was deployed in the submarine spring (Kiveri) for continuous monitoring...     

PET Diagnostic Molecules Utilizing Multimeric Cyclic RGD Peptide Analogs for Imaging Integrin αvβ3 Receptors

Multimeric ligands consisting of multiple pharmacophores connected to a single backbone have been widely investigated for diagnostic and therapeutic applications. In this review, we summarize recent developments regarding multimeric radioligands targeting integrin α_vβ₃ receptors on cancer cells for molecular imaging and diagnostic applications using positron emission tomography (PET). Integrin α_vβ₃ receptors are glycoproteins expressed on the cell surface, which have a significant role in tumor angiogenesis. They act as receptors for several extracellular matrix proteins exposing the tripeptide sequence arginine-glycine-aspartic (RGD). Cyclic RDG peptidic ligands c(RGD) have been developed for integrin α_vβ₃ tumor-targeting positron emission tomography (PET) diagnosis. Several c(RGD) pharmacophores, connected with the linker and conjugated to a chelator or precursor for radiolabeling with different PET radionuclides (¹⁸F, ⁶⁴Cu, and ⁶⁸Ga), have resulted in multimeric ligands superior to c(RGD) monomers. The binding avidity, pharmacodynamic, and PET imaging properties of these multimeric c(RGD) radioligands, in relation to their structural characteristics are analyzed and discussed. Furthermore, specific examples from preclinical studies and clinical investigations are included.