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non monotonicity close convex shape neural computer code neural code list subset neuron fire together picky interestingness neuron called place cell fervency animal specific usually convex region space fundamental question therefore determine neuronic code arise region collection open convex set closed convex set euclidean space work focus two course study computer code open convex closed convex computer code related starting point open convex code desirable monotonicity holding wit adding non maximal codewords preserve open convexity show property fails hold closed convex computer code additionally lend non maximal codewords increase undefendable imbed dimension demonstrate adding individual codeword increase closed embedding proportion arbitrarily large sum last disprove conjecture goldrup phillipson well present example computer code neither open convex closed convex

shortcut adiabaticity concept method lotion shortcut adiabaticity sta fast route final result slow adiabatic change controlling parameter system shortcut designed set analytical numerical method acting suitable different system condition motivation apply sta method quantum arrangement manipulate timescales shorter decoherence time thus shortcut adiabaticity suit implemental train driving internal motional state department nuclear molecular solid state physic application range information transfer processing ground gate analog paradigm interferometry metrology numerosity sta path controlling parameter english hawthorn use heighten robustness versus noise perturbation optimize relevant variable since adiabaticity widespread phenomenon sta method also extended beyond quantum world optical device classical mechanical system statistical physic cutoff adiabaticity combine well concept technique particular optimal control possibility pose profound scientific engineering question finding swiftness limit quantify third law determining process energy monetary value efficiency concept method application shortcut adiabaticity reviewed bright prospect outlined well open question challenge ahead

tst black string study relationship tst transformation bare deformation string theory ad background irrelevant contortion cfts show tst shift n background correspond instant distortion worldsheet action antisymmetric cartesian product two emmy noether current holographically mirroring definition deformation cfts apply tst transformation string theory btz obtain worldwide class rotating black string solution including horne horowitz giveon itzhaki kutasov one particular typesetter case show holographically dual caloric state single trace deformed cfts also discover smooth solution alter globular ad ir linear dilaton setting uv interpreted n ground re publica dual deformed cft backdrop intimate existence upper bound distortion parameter answer becomes complex find worldsheet spectrum thermodynamics black string particular bekenstein hawking entropy critical value contortion parameter match corresponding quantity obtained single trace deformation