Finite-length Patents and Functional Differential Equations in a Non-scale R&D-based Growth Model

The statutory patent length is 20 years in most countries. R&D-based endogenous growth models, however, often presume an infinite patent length. In this paper, finite-length patents are embedded in a non-scale R&D-based growth model, but any patent’s effective life may be terminated prematurely at any moment, subject to two idiosyncratic hazards of imitation and innovation. This gives rise to an autonomous system of mixed-type functional differential equations (FDEs). Its dynamics are driven by current, delayed and advanced states. We present an algorithm to solve the FDEs by solving a sequence of standard BVPs (boundary value problems) for systems of ODEs (ordinary differential equations). We use this algorithm to simulate a calibrated U.S. economy’s transitional dynamics by making discrete changes from the baseline 20 years patent length. We find that if transitional impacts are taken into account, optimizing the patent length incurs a welfare loss, albeit rather small. This suggests that fine-tuning the world’s patent systems may not be a worthwhile effort

Finite-length Patents and Functional Differential Equations in a Non-scale R&D-based Growth Model

The statutory patent length is 20 years in most countries. R&D-based endogenous growth models, however, often presume an infinite patent length. In this paper, finite-length patents are embedded in a non-scale R&D-based growth model, but any patent’s effective life may be terminated prematurely at any moment, subject to two idiosyncratic hazards of imitation and innovation. This gives rise to an autonomous system of mixed-type functional differential equations (FDEs). Its dynamics are driven by current, delayed and advanced states. We present an algorithm to solve the FDEs by solving a sequence of standard BVPs (boundary value problems) for systems of ODEs (ordinary differential equations). We use this algorithm to simulate a calibrated U.S. economy’s transitional dynamics by making discrete changes from the baseline 20 years patent length. We find that if transitional impacts are taken into account, optimizing the patent length incurs a welfare loss, albeit rather small. This suggests that fine-tuning the world’s patent systems may not be a worthwhile effort

Heat to Electricity Conversion by a Graphene Stripe with Heavy Chiral Fermions

A conversion of thermal energy into electricity is considered in the electrically polarized graphene stripes with zigzag edges where the heavy chiral fermion (HCF) states are formed. The stripes are characterized by a high electric conductance Ge and by a significant Seebeck coefficient S. The electric current in the stripes is induced due to a non-equilibrium thermal injection of "hot" electrons. This thermoelectric generation process might be utilized for building of thermoelectric generators with an exceptionally high figure of merit Z{\delta}T \simeq 100 >> 1 and with an appreciable electric power densities \sim 1 MW/cm2.Comment: 8 pages, 3 figure

On the existence of supergravity duals to D1--D5 CFT states

We define a metric operator in the 1/2-BPS sector of the D1-D5 CFT, the eigenstates of which have a good semi-classical supergravity dual; the non-eigenstates cannot be mapped to semi-classical gravity duals. We also analyse how the data defining a CFT state manifests itself in the gravity side, and show that it is arranged into a set of multipoles. Interestingly, we find that quantum mechanical interference in the CFT can have observable manifestations in the semi-classical gravity dual. We also point out that the multipoles associated to the normal statistical ensemble fluctuate wildly, indicating that the mixed thermal state should not be associated to a semi-classical geometry.Comment: 22 pages, 2 figures. v2 : references added, typos correcte

A Parallelizable Heuristic for Solving the Generic Materials and Operations Planning in a Supply Chain Network: A Case Study from the Automotive Industry

[EN] A trend in up-to date developments in multi-site operations planning models is to consider in details the different ways to produce, buy or transport products and the distributed decision-making process for operations planning. One of the most generic approaches to support global optimization in those supply chain networks by considering all the different operations alternatives and product structures is the Generic Materials & Operations Planning Problem. This problem can be modelled by a Mixed Integer Linear Programming model capable of considering production, transportation, procurement tasks and their alternatives and other relevant issues such as packaging. The aim of this paper is to introduce the implementation of a parallelizable heuristic method for materials and operations planning and its application to a case of a Supply Chain Network of the automotive industry. The approach uses variants of the GMOP model to overcome traditional MRP systems' limitations.Maheut ., JP.; García Sabater, JP. (2013). A Parallelizable Heuristic for Solving the Generic Materials and Operations Planning in a Supply Chain Network: A Case Study from the Automotive Industry. IFIP Advances in Information and Communication Technology. 397:151-157. doi:10.1007/978-3-642-40352-1_20S151157397Maheut, J., Garcia-Sabater, J.P.: La Matriz de Operaciones y Materiales y la Matriz de Operaciones y Recursos, un nuevo enfoque para resolver el problema GMOP basado en el concepto del Stroke. Dirección y Organización 45, 46–57 (2011)Garcia-Sabater, J.P., Maheut, J., Marin-Garcia, J.A.: A new formulation technique to model Materials and Operations Planning: the Generic Materials and Operations Planning (GMOP) Problem. European J. Industrial Engineering 7, 119–147 (2013)Mula, J., Maheut, J., Garcia-Sabater, J.P.: Supply Chain Network Design. Journal of Marketing and Operations Management Research 1, 378–383 (2012)Dudek, G., Stadtler, H.: Negotiation-based collaborative planning between supply chains partners. European Journal of Operational Research 163, 668–687 (2005)Torabi, S.A., Hassini, E.: Multi-site production planning integrating procurement and distribution plans in multi-echelon supply chains: an interactive fuzzy goal programming approach. International Journal of Production Research 47, 5475–5499 (2009)Kanyalkar, A.P., Adil, G.K.: Aggregate and detailed production planning integrating procurement and distribution plans in a multi-site environment. International Journal of Production Research 45, 5329–5353 (2007)de Kok, T.G., Fransoo, J.C.: Planning Supply Chain Operations: Definition and Comparison of Planning Concepts. In: Graves, S.C. (ed.) Handbooks in Operations Research and Management Science Supply Chain Management: Design, Coordination and Operation, vol. 11, pp. 597–675. Elsevier (2003)Buschkühl, L., Sahling, F., Helber, S., Tempelmeier, H.: Dynamic capacitated lot-sizing problems: a classification and review of solution approaches. OR Spectrum (2009)Maheut, J., Garcia-Sabater, J.P., Mula, J.: A supply Chain Operations Lot-Sizing and Scheduling Model with Alternative Operations. In: Sethi, S.P., Bogataj, M., Ros-McDonnell, L. (eds.) Proceedings of the Industrial Engineering: Innovative Networks, 5th International Conference on Industrial Engineering and Industrial Management "CIO 2011", Cartagena, Spain, pp. 309–316. Springer, London (2012)Garcia-Sabater, J.P., Maheut, J., Garcia-Sabater, J.J.: A two-stage sequential planning scheme for integrated operations planning and scheduling system using MILP: the case of an engine assembler. Flexible Services and Manufacturing Journal 24, 171–209 (2012)Pinto, J.M., Chen, P., Papageorgiou, L.G.: A discrete/continuous time MILP model for medium term planning of single stage multiproduct plants, pp. 1–6. Elsevier, B.V. (2007)Scheer, A.W.: Business Process Engineering - Reference Models for Industrial Enterprises. Springer (1994)Lin, J.T., Chen, T.L., Lin, Y.T.: Critical material planning for TFT-LCD production industry. International Journal of Production Economics 122, 639–655 (2009)Escudero, L.F.: CMIT, capacitated multi-level implosion tool. European Journal of Operational Research 76, 511–528 (1994)Maheut, J., Garcia-Sabater, J.P., Valero-Herrero, M.: MILP model for solving the supply chain operations scheduling problem with alternative operations considering delay penalization: a case study of a mass customization company. In: Proceedings of the 41st International Conference on Computers & Industrial Engineering, pp. 289–294 (2011

Loop operators and S-duality from curves on Riemann surfaces

We study Wilson-'t Hooft loop operators in a class of N=2 superconformal field theories recently introduced by Gaiotto. In the case that the gauge group is a product of SU(2) groups, we classify all possible loop operators in terms of their electric and magnetic charges subject to the Dirac quantization condition. We then show that this precisely matches Dehn's classification of homotopy classes of non-self-intersecting curves on an associated Riemann surface--the same surface which characterizes the gauge theory. Our analysis provides an explicit prediction for the action of S-duality on loop operators in these theories which we check against the known duality transformation in several examples.Comment: 41 page

Entanglement, quantum phase transition and scaling in XXZ chain

Motivated by recent development in quantum entanglement, we study relations among concurrence $C$, SU$_q$(2) algebra, quantum phase transition and correlation length at the zero temperature for the XXZ chain. We find that at the SU(2) point, the ground state possess the maximum concurrence. When the anisotropic parameter $\Delta$ is deformed, however, its value decreases. Its dependence on $\Delta$ scales as $C=C_0-C_1(\Delta-1)^2$ in the XY metallic phase and near the critical point (i.e. $1<\Delta<1.3$) of the Ising-like insulating phase. We also study the dependence of $C$ on the correlation length $\xi$, and show that it satisfies $C=C_0-1/2\xi$ near the critical point. For different size of the system, we show that there exists a universal scaling function of $C$ with respect to the correlation length $\xi$.Comment: 4 pages, 3 figures. to appear in Phys. Rev.

Quantum geometry and gravitational entropy

Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S^5 universes. In this sector we devise a "coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.Comment: 29 pages, 2 figures; references adde