No-Forcing and No-Matching Theorems for Classical Probability Applied to Quantum Mechanics

Correlations of spins in a system of entangled particles are inconsistent with Kolmogorov’s probability theory (KPT), provided the system is assumed to be non-contextual. In the Alice–Bob EPR paradigm, non-contextuality means that the identity of Alice’s spin (i.e., the probability space on which it is defined as a random variable) is determined only by the axis $\alpha _{i}$ chosen by Alice, irrespective of Bob’s axis $\beta _{j}$ (and vice versa). Here, we study contextual KPT models, with two properties: (1) Alice’s and Bob’s spins are identified as $A_{ij}$ and $B_{ij}$ , even though their distributions are determined by, respectively, $\alpha _{i}$ alone and $\beta _{j}$ alone, in accordance with the no-signaling requirement; and (2) the joint distributions of the spins $A_{ij},B_{ij}$ across all values of $\alpha _{i},\beta _{j}$ are constrained by fixing distributions of some subsets thereof. Of special interest among these subsets is the set of probabilistic connections, defined as the pairs $\left( A_{ij},A_{ij'}\right) $ and $\left( B_{ij},B_{i'j}\right) $ with $\alpha _{i}\not =\alpha _{i'}$ and $\beta _{j}\not =\beta _{j'}$ (the non-contextuality assumption is obtained as a special case of connections, with zero probabilities of $A_{ij}\not =A_{ij'}$ and $B_{ij}\not =B_{i'j}$ ). Thus, one can achieve a complete KPT characterization of the Bell-type inequalities, or Tsirelson’s inequalities, by specifying the distributions of probabilistic connections compatible with those and only those spin pairs $\left( A_{ij},B_{ij}\right) $ that are subject to these inequalities. We show, however, that quantum-mechanical (QM) constraints are special. No-forcing theorem says that if a set of probabilistic connections is not compatible with correlations violating QM, then it is compatible only with the classical–mechanical correlations. No-matching theorem says that there are no subsets of the spin variables $A_{ij},B_{ij}$ whose distributions can be fixed to be compatible with and only with QM-compliant correlations.     

Geospatial model of COVID-19 spreading and vaccination with event Gillespie algorithm

We have developed a mathematical model and stochastic numerical simulation for the transmission of COVID-19 and other similar infectious diseases that accounts for the geographic distribution of population density, detailed down to the level of location of individuals, and age-structured contact rates. Our analytical framework includes a surrogate model optimization process to rapidly fit the parameters of the model to the observed epidemic curves for cases, hospitalizations, and deaths. This toolkit (the model, the simulation code, and the optimizer) is a useful tool for policy makers and epidemic response teams, who can use it to forecast epidemic development scenarios in local settings (at the scale of cities to large countries) and design optimal response strategies. The simulation code also enables spatial visualization, where detailed views of epidemic scenarios are displayed directly on maps of population density. The model and simulation also include the vaccination process, which can be tailored to different levels of efficiency and efficacy of different vaccines. We used the developed framework to generate predictions for the spread of COVID-19 in the canton of Geneva, Switzerland, and validated them by comparing the calculated number of cases and recoveries with data from local seroprevalence studies.

     

Molecular Engineering of Fracture Energy Dissipating Sacrificial Bonds Into Cellulose Nanocrystal Nanocomposites

Even though nanocomposites have provided a plethora of routes to increase stiffness and strength, achieving increased toughness with suppressed catastrophic crack growth has remained more challenging. Inspired by the concepts of mechanically excellent natural nanomaterials, one‐component nanocomposites were fabricated involving reinforcing colloidal nanorod cores with polymeric grafts containing supramolecular binding units. The concept is based on mechanically strong native cellulose nanocrystals (CNC) grafted with glassy polymethacrylate polymers, with side chains that contain 2‐ureido‐4[1H]‐pyrimidone (UPy) pendant groups. The interdigitation of the grafts and the ensuing UPy hydrogen bonds bind the nanocomposite network together. Under stress, UPy groups act as sacrificial bonds: simultaneously providing adhesion between the CNCs while allowing them to first orient and then gradually slide past each other, thus dissipating fracture energy. We propose that this architecture involving supramolecular binding units within side chains of polymer grafts attached to colloidal reinforcements opens generic approaches for tough nanocomposites.     

Blocking the lateral film growth at the nanoscale in area-selective atomic layer deposition

Area-selective atomic layer deposition (ALD) allows the growth of highly uniform thin inorganic films on certain parts of the substrate while preventing the film growth on other parts. Although the selective ALD growth is working well at the micron and submicron scale, it has failed at the nanoscale, especially near the interface where there is growth on one side and no-growth on the other side. The reason is that methods so far solely rely on the chemical modification of the substrate, while neglecting the occurrence of lateral ALD growth at the nanoscale. Here we present a proof-of-concept for blocking the lateral ALD growth also at the nanoscale by combining the chemical surface modification with topographical features. We demonstrate that area-selective ALD of ZnO occurs by applying the diethylzinc/water ALD process on cicada wings that contain a dense array of nanoscopic pillars. The sizes of the features in the inorganic film are down to 25 nm which is, to the best of our knowledge, the smallest obtained by area-selective ALD. Importantly, our concept allows the synthesis of such small features even though the film is multiple times thicker.     

Modification of carbonic anhydrase II with acetaldehyde, the first metabolite of ethanol, leads to decreased enzyme activity

Background

Bacillus thuringiensis Cry1Aa insecticidal protein is the most active known B. thuringiensis toxin against the forest insect pest Lymantria dispar (gypsy moth), unfortunately it is also highly toxic against the non-target insect Bombyx mori (silk worm).

Results

Surface exposed hydrophobic residues over domains II and III were targeted for site-directed mutagenesis. Substitution of a phenylalanine residue (F328) by alanine reduced binding to the Bombyx mori cadherin by 23-fold, reduced biological activity against B. mori by 4-fold, while retaining activity against Lymantria dispar.

Conclusion

The results identify a novel receptor-binding epitope and demonstrate that virtual elimination of binding to cadherin BR-175 does not completely remove toxicity in the case of B. mori.     

Oxidation of a laccase mediator ABTS as studied by ESI-FTICR mass spectrometry

The oxidation reaction of a laccase mediator ABTS (2,2'-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) was studied by electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI-FTICRMS). Oxidation products of ABTS were measured after reaction times that varied from a few minutes up to several days and both positive and negative ionization modes were employed. Exact mass measurements and collision-induced dissociation (CID) experiments were used to characterize the structures of the ions formed. After reacting with Trametes versicolor laccase (TvL), the radical cation form of ABTS was the main product observed by the positive ionization mode. Negative ionization mode experiments revealed that a degradation product from ABTS was formed.     

Noncovalent Complexation of Monoamine Neurotransmitters and Related Ammonium Ions by Tetramethoxy Tetraglucosylcalix[4]arene

The noncovalent complexation of monoamine neurotransmitters and related ammonium and quaternary ammonium ions by a conformationally flexible tetramethoxy glucosylcalix[4]arene was studied by electrospray ionization Fourier transform ion cyclotron resonance (ESI-FTICR) mass spectrometry. The glucosylcalixarene exhibited highest binding affinity towards serotonin, norepinephrine, epinephrine, and dopamine. Structural properties of the guests, such as the number, location, and type of hydrogen bonding groups, length of the alkyl spacer between the ammonium head-group and the aromatic ring structure, and the degree of nitrogen substitution affected the complexation. Competition experiments and guest-exchange reactions indicated that the hydroxyl groups of guests participate in intermolecular hydrogen bonding with the glucocalixarene.     

Two-dimensional-Raman-terahertz spectroscopy of water: theory

We discuss the hybrid 2D-Raman-THz spectroscopy of liquid water. This two-dimensional spectroscopy is designed to directly work in the low-frequency range of the intermolecular degrees of freedom. The information content of 2D-Raman-THz spectroscopy is similar to 2D-Raman or 2D-THz spectroscopy, but its experimental implementation should be easier. That is, 2D-Raman-THz spectroscopy is a 3rd-order nonlinear spectroscopy and as such completely avoids cascading of consecutive 3rd-order signals, which turned out to be a major difficulty in 5th-order 2D-Raman spectroscopy. On the other hand, it does not require any intense THz pump-pulse, the lack of which limits 2D-THz spectroscopy to the study of semiconductor quantum wells as the currently available pulse energies are too low for molecular systems. In close analogy to 2D-Raman spectroscopy, the 2D-Raman-THz response of liquid water is simulated from an all-atom molecular dynamics simulation, and the expected spectral features are discussed.     

Fast Growing Solutions of Linear Differential Equations in the Unit Disc

For $n \in \mathbb{N}$ , the n-order of an analytic function f in the unit disc D is defined by $$\sigma _{{{M,n}}} (f) = {\mathop {\lim \sup }\limits_{r \to 1^{ - } } }\frac{{\log ^{ + }_{{n + 1}} M(r,f)}} {{ - \log (1 - r)}},$$ where log⁺ x  =  max{log x, 0}, log ⁺ ₁ x  =  log ⁺ x, log ⁺ _n+1 x  =  log ⁺ log ⁺ _n x, and M(r, f) is the maximum modulus of f on the circle of radius r centered at the origin. It is shown, for example, that the solutions f of the complex linear differential equation $$f^{{(k)}} + a_{{k - 1}} (z)f^{{(k - 1)}} + \cdots + a_{1} (z)f^{\prime} + a_{0} (z)f = 0,\quad \quad \quad (\dag)$$ where the coefficients are analytic in D, satisfy σ _M,n+1(f)  ≤  α if and only if σ _M,n (a _j )  ≤  α for all j  =  0, ..., k ? 1. Moreover, if q ∈{0, ..., k ? 1} is the largest index for which $\sigma _{M,n} ( a_{q}) = {\mathop {\max }\limits_{0 \leq j \leq k - 1} }{\left\{ {\sigma _{{M,n}} {\left( {a_{j} } \right)}} \right\}}$ , then there are at least k ? q linearly independent solutions f of ( $\dag$ ) such that σ _M,n+1(f) = σ _M,n (a _q ). Some refinements of these results in terms of the n-type of an analytic function in D are also given.     

Pump-probe and pump-deplete-probe spectroscopies on carotenoids with N=9-15 conjugated bonds

A series of all-trans-carotenoids with N=9, 13, and 15 conjugated bonds has been studied by pump-probe and pump-deplete-probe spectroscopies to obtain a systematic analysis of the energy flow between the different electronic states. The ultrafast dynamics in the carotenoids are initialized by excitation to the S2 state and subsequently manipulated by an additional depletion pulse in the near-IR spectral range. The changes in the dynamics after depletion of the excited state population allowed differentiation of the excited state absorption into two components, a major one corresponding to the well known S1 state and the small contribution on the red wing of the S0-S2 absorption band originating from the hot ground state. We found no evidence for an additional electronically excited state, usually called S*. Instead, a deactivation mechanism that includes the hot ground state supports the observed results nicely in the framework of a simple three state model (S2, S1, and S0).