Fixed-Size Quadruples for a New, Hardware-Oriented Representation of the 4D Clifford Algebra

Clifford algebra (geometric algebra) offers a natural and intuitive way to model geometry in fields as robotics, machine vision and computer graphics. This paper proposes a new representation based on fixed-size elements (quadruples) of 4D Clifford algebra and demonstrates that this choice leads to an algorithmic simplification which in turn leads to a simpler and more compact hardware implementation of the algebraic operations. In order to prove the advantages of the new, quadruple-based representation over the classical representation based on homogeneous elements, a coprocessing core supporting the new fixed-size Clifford operands, namely Quad-CliffoSor (Quadruple-based Clifford coprocesSor) was designed and prototyped on an FPGA board. Test results show the potential to achieve a 23× speedup for Clifford products and a 33× speedup for Clifford sums and differences compared to the same operations executed by a software library running on a general-purpose processor.     

Synthesis of poly(urethane urea) by in situ polymerization inside stone

The first synthesis of poly(urethane urea) by in situ polymerization inside stone was successfully carried out. Poly(propylene glycol), isophorondiisocyanate, and a catalyst [tin(II) ethyl hexanoate, aluminum acetylacetonate, or zirconium acetylacetonate] were mixed with acetone in petri dishes, and tuff samples were placed in the dishes at room temperature. The effects of the comonomer ratio, catalyst, and catalyst concentration on the chemical structure of the synthesized poly(urethane urea) were investigated. The poly(urethane urea) distribution inside the tuff and the related morphology were also analyzed, as well as the reversibility of the performed treatments. Finally, the effects of the in situ polymerization polymer on the properties of the stone, such as water capillary absorption and permeability to water vapor, were assessed. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 542–552, 2005     

The synthesis and reactivity of some 2-amino-5-bromo-],1,3,4-thiadiazoles and the corresponding Δ2-1,3,4-thiadiazolines

The synthesis of some 2-amino-5-bromo-1,3,4-thiadiazoles is reported; these substrates are found to behave as ambidenl nucleophiles in alkylation, aeylation and nitrosation reactions, giving thiadiazoliens along with thiadiazole derivatives. This finding suggests amine-imine tautomerism between these compounds and the corresponding Δ²-1,3,4-thiadiazolines.     

Systems of p-Laplacian differential inclusions with large diffusion

In this paper we consider coupled systems of p-Laplacian differential inclusions and we prove, under suitable conditions, that a homogenization process occurs when diffusion parameters become arbitrarily large. In fact we obtain that the attractors are continuous at infinity on L²(Ω)×L²(Ω) topology, with respect to the diffusion coefficients, and the limit set is the attractor of an ordinary differential problem.     

Fermionic wigs for BTZ black holes

We compute the wig for the BTZ black hole, namely the complete non-linear solution of supergravity equations with all fermionic zero modes. We use a “gauge completion” method starting from _AdS3${\mathit{AdS}}_3$ Killing spinors to generate the gravitinos fields associated to the BH and we compute the back-reaction on the metric. Due to the anticommutative properties of the fermionic hairs the resummation of these effects truncates at some order. We illustrate the technique proposed in a precedent paper in a very explicit and analytical form. We also compute the mass, the angular momentum and other charges with their corrections.     

How deeply are core electrons perturbed when valence electrons are spin polarized? The case study of transition metal compounds

The ferromagnetic and antiferromagnetic wave functions of the KMnF₃ perovskite have been evaluated quantum-mechanically by using an all electron approach and, for comparison, pseudopotentials on the transition metal and the fluorine ions. It is shown that the different number of α and β electrons in the d shell of Mn perturbs the inner shells, with shifts between the α and β eigenvalues that can be as large as 6 eV for the 3s level, and is far from negligible also for the 2s and 2p states. The valence electrons of F are polarized by the majority spin electrons of Mn, and in turn, spin polarize their 1s electrons. When a pseudopotential is used, such a spin polarization of the core functions of Mn and F can obviously not take place. The importance of such a spin polarization can be appreciated by comparing (i) the spin density at the Mn and F nuclear position, and then the Fermi contact constant, a crucial quantity for the hyperfine coupling, and (ii) the ferromagnetic–antiferromagnetic energy difference, when obtained with an all electron or a pseudopotential scheme, and exploring how the latter varies with pressure. This difference is as large as 50% of the all electron datum, and is mainly due to the rigid treatment of the F ion core. The effect of five different functionals on the core spin polarization is documented.     

On Attractors for Multivalued Semigroups Defined by Generalized Semiflows

In this paper we extend results from Semigroup Theory on existence and characterization of attractors in order to include multivalued semigroups T(t) defined by generalized semiflows . In particular we show that, if is continuous, possesses a Lyapunov function, and has a global attractor which is maximal compact invariant, then  =  W ^u (Z()), where Z() is the stationary solutions set and W ^u (Z()) is the unstable set of Z(). We introduce the -attractor concept which does not enjoy any uniformity on time of attraction and we prove, under suitable conditions, that the global -attractor is the set of asymptotic states described by Z(). Jacson Simsen is supported by CAPES-Brazil.     

Decorated DNA-Based Scaffolds as Lateral Flow Biosensors

Here we develop Lateral Flow Assays (LFAs) that employ as functional elements DNA-based structures decorated with reporter tags and recognition elements. We have rationally re-engineered tile-based DNA tubular structures that can act as scaffolds and can be decorated with recognition elements of different nature (i.e. antigens, aptamers or proteins) and with orthogonal fluorescent dyes. As a proof-of-principle we have developed sandwich and competitive multiplex lateral flow platforms for the detection of several targets, ranging from small molecules (digoxigenin, Dig and dinitrophenol, DNP), to antibodies (Anti-Dig, Anti-DNP and Anti-MUC1/EGFR bispecific antibodies) and proteins (thrombin). Coupling the advantages of functional DNA-based scaffolds together with the simplicity of LFAs, our approach offers the opportunity to detect a wide range of targets with nanomolar sensitivity and high specificity.     

An investigation on calcium (II) oxalate as solubility and universal standard

The investigation on calcium (II) oxalate is carried out in order to study its solubility in different ionic media. In the same conditions the protonation constants of oxalate and the stability of complex species have been determined. As the stoichiometric composition of the solid calcium (II) oxalate prepared for the investigation was accurately checked, the salt CaC2O4 x H2O is proposed as universal (chelometry, redox, acidimetry) standard. Results of titrations support this possibility.     

Automated discovery of noncovalent inhibitors of SARS-CoV-2 main protease by consensus Deep Docking of 40 billion small molecules

Recent explosive growth of ‘make-on-demand’ chemical libraries brought unprecedented opportunities but also significant challenges to the field of computer-aided drug discovery. To address this expansion of the accessible chemical universe, molecular docking needs to accurately rank billions of chemical structures, calling for the development of automated hit-selecting protocols to minimize human intervention and error. Herein, we report the development of an artificial intelligence-driven virtual screening pipeline that utilizes Deep Docking with Autodock GPU, Glide SP, FRED, ICM and QuickVina2 programs to screen 40 billion molecules against SARS-CoV-2 main protease (Mpro). This campaign returned a significant number of experimentally confirmed inhibitors of Mpro enzyme, and also enabled to benchmark the performance of twenty-eight hit-selecting strategies of various degrees of stringency and automation. These findings provide new starting scaffolds for hit-to-lead optimization campaigns against Mpro and encourage the development of fully automated end-to-end drug discovery protocols integrating machine learning and human expertise.

Deep learning-accelerated docking coupled with computational hit selection strategies enable the identification of inhibitors for the SARS-CoV-2 main protease from a chemical library of 40 billion small molecules.