ChatGPT in a Contract Drafting Class

Our presentation will discuss the impact of ChatGPT on contract drafting pedagogy. Specifically, we will examine ChatGPT’s basis of knowledge and whether it has sufficient theoretical foundation to be used as a pedagogical tool; whether ChatGPT’s practical application supports proven methods of instructional delivery; and ChatGPT’s functionality as an assessment tool. 1. ChatGPT’s basis of knowledge and whether it has sufficient theoretical foundation to be used as a pedagogical tool Our presentation will compare the pretraining of ChatGPT and to the typical Contract Drafting pedagogy. We will start by showing the program on a screen and asking it how it was trained and what principles it follows to draft contracts. We will then compare this to the principles students are taught to apply in a typical contract drafting class. Our working hypotheses is that ChatGPT draws from internet resources and follows basic principles of clear writing. In contrast, transactional attorneys typically either draft from scratch following whatever conventions they were trained on, or they start with a form or sample document and then revise it for a specific transaction. 2. Whether ChatGPT’s practical application supports proven methods of instructional delivery We will then show an example of how ChatGPT works by giving it a prompt that would be typical in any contract drafting class and asking it to draft the applicable contract from scratch. It takes less than a minute for the program to draft the type of contract students typically draft in class. We will examine the sufficiency of ChatGPT’s output. The next step will be to highlight errors and other issues with the document ChatGPT drafts. We will ask the program if it can draft the contract following certain conventions (since drafting courses are typically taught according to conventions) and see whether it can actually do what it says it can do (it can’t). Ultimately, we will look at techniques that can be used to improve the quality and completeness of the documents ChatGPT produces so that it aligns more with the way contract drafting classes are typically taught. The program works better, for example, if you ask more specific questions and provide feedback on the output

Extended Symbolic Dynamics in Bistable CML: Existence and Stability of Fronts

We consider a diffusive Coupled Map Lattice (CML) for which the local map is piece-wise affine and has two stable fixed points. By introducing a spatio-temporal coding, we prove the one-to-one correspondence between the set of global orbits and the set of admissible codes. This relationship is applied to the study of the (uniform) fronts' dynamics. It is shown that, for any given velocity in $[-1,1]$, there is a parameter set for which the fronts with that velocity exist and their shape is unique. The dependence of the velocity of the fronts on the local map's discontinuity is proved to be a Devil's staircase. Moreover, the linear stability of the global orbits which do not reach the discontinuity follows directly from our simple map. For the fronts, this statement is improved and as a consequence, the velocity of all the propagating interfaces is computed for any parameter. The fronts are shown to be also nonlinearly stable under some restrictions on the parameters. Actually, these restrictions follow from the co-existence of uniform fronts and non-uniformly travelling fronts for strong coupling. Finally, these results are extended to some $C^{\infty}$ local maps.Comment: 27 pages, Latex, 2 figure

Unconventional superconductivity near a flat band in organic and organometallic materials

We study electron correlation driven superconductivity on a decorated honeycomb lattice (DHL), which has a low-energy flat band. On doping, we find singlet superconductivity with extended-s, extended-d and f-wave symmetry mediated by magnetic exchange. f-wave singlet pairing is enabled by the lattice decoration. The critical temperature is predicted to be significantly higher than on similar lattices lacking flat bands. We discuss how high-temperature superconductivity could be realized in the DHL materials such as Rb3TT. 2 H2O and Mo3S7(dmit)3.Comment: 4 pages, 4 figures + Supplemental materia

Survival probabilities in time-dependent random walks

We analyze the dynamics of random walks in which the jumping probabilities are periodic {\it time-dependent} functions. In particular, we determine the survival probability of biased walkers who are drifted towards an absorbing boundary. The typical life-time of the walkers is found to decrease with an increment of the oscillation amplitude of the jumping probabilities. We discuss the applicability of the results in the context of complex adaptive systems.Comment: 4 pages, 3 figure

Survival Probabilities of History-Dependent Random Walks

We analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations) in the presence of an absorbing boundary. An analytically solvable model is presented, in which a dynamical phase-transition occurs when the correlation strength parameter \mu reaches a critical value \mu_c. For strong positive correlations, \mu > \mu_c, the survival probability is asymptotically finite, whereas for \mu < \mu_c it decays as a power-law in time (chain length).Comment: 3 pages, 2 figure

Phase-Transition in Binary Sequences with Long-Range Correlations

Motivated by novel results in the theory of correlated sequences, we analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations). In our model, the probability for a unit bit in a binary string depends on the fraction of unities preceding it. We show that the system undergoes a dynamical phase-transition from normal diffusion, in which the variance D_L scales as the string's length L, into a super-diffusion phase (D_L ~ L^{1+|alpha|}), when the correlation strength exceeds a critical value. We demonstrate the generality of our results with respect to alternative models, and discuss their applicability to various data, such as coarse-grained DNA sequences, written texts, and financial data.Comment: 4 pages, 4 figure

Detecting Molecular Rotational Dynamics Complementing the Low-Frequency Terahertz Vibrations in a Zirconium-Based Metal-Organic Framework

We show clear experimental evidence of co-operative terahertz (THz) dynamics observed below 3 THz (~100 cm-1), for a low-symmetry Zr-based metal-organic framework (MOF) structure, termed MIL-140A [ZrO(O2C-C6H4-CO2)]. Utilizing a combination of high-resolution inelastic neutron scattering and synchrotron radiation far-infrared spectroscopy, we measured low-energy vibrations originating from the hindered rotations of organic linkers, whose energy barriers and detailed dynamics have been elucidated via ab initio density functional theory (DFT) calculations. For completeness, we obtained Raman spectra and characterized the alterations to the complex pore architecture caused by the THz rotations. We discovered an array of soft modes with trampoline-like motions, which could potentially be the source of anomalous mechanical phenomena, such as negative linear compressibility and negative thermal expansion. Our results also demonstrate coordinated shear dynamics (~2.5 THz), a mechanism which we have shown to destabilize MOF crystals, in the exact crystallographic direction of the minimum shear modulus (Gmin).Comment: 10 pages, 6 figure

Experimental verification of the usefulness of the nth power law MOSFET model under hot carrier wearout

4 pagesInternational audienceIn this paper the usefulness of the nth power law MOSFET model under Hot Carrier Injection (HCI) wearout has been experimentally demonstrated. In order to do that, three types of nFET transistors have been analyzed under different HCI conditions and the nth power law MOSFET model has been extracted for each sample. The results show that the model can reproduce the MOSFET behavior under HCI wearout mechanism. Therefore, the impact of HCI on circuits can be analyzed by using the nth power law MOSFET model

Metastable states, quasi-stationary distributions and soft measures

We establish metastability in the sense of Lebowitz and Penrose under practical and simple hypothesis for (families of) Markov chains on finite configuration space in some asymptotic regime, including the case of configuration space size going to infinity. By comparing restricted ensemble and quasi-stationary measures, we study point-wise convergence velocity of Yaglom limits and prove asymptotic exponential exit law. We introduce soft measures as interpolation between restricted ensemble and quasi-stationary measure to prove an asymptotic exponential transition law on a generally different time scale. By using potential theoretic tools, we prove a new general Poincar\'e inequality and give sharp estimates via two-sided variational principles on relaxation time as well as mean exit time and transition time. We also establish local thermalization on a shorter time scale and give mixing time asymptotics up to a constant factor through a two-sided variational principal. All our asymptotics are given with explicit quantitative bounds on the corrective terms.Comment: 41 page

Catalytic asymmetric conjugate addition of dialkylzinc reagents to alpha,beta-unsaturated sulfones

An efficient method is reported for the highly enantioselective copper-catalyzed conjugate addition of dialkylzinc reagents to α,β-unsaturated sulfones using a monodentate phosphoramidite ligand.