They allow speech signals to be processed time- invariantly. In 1990 Hampshire and Waibel introduced a variant which performs a two dimensional convolution.John B. Hampshire and Alexander Waibel, Connectionist Architectures for Multi-Speaker Phoneme Recognition, Advances in Neural Information Processing Systems, 1990, Morgan Kaufmann. Since these TDNNs operated on spectrograms, the resulting phoneme recognition system was invariant to both shifts in time and in frequency.
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In mathematics, specifically group theory, a subgroup series is a chain of subgroups: :1 = A_0 \leq A_1 \leq \cdots \leq A_n = G. Subgroup series can simplify the study of a group to the study of simpler subgroups and their relations, and several subgroup series can be invariantly defined and are important invariants of groups. A subgroup series is used in the subgroup method. Subgroup series are a special example of the use of filtrations in abstract algebra.
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Dybo's law, or Dybo–Illich-Svitych's law, is a Common Slavic accent law named after Russian accentologists Vladimir Dybo and Vladislav Illich-Svitych. It was posited to explain the occurrence of nouns and verbs in Slavic languages which are invariantly accented on the inflectional ending. The latter is seen as an innovation from the original Proto-Balto-Slavic accent system, in which nouns and verbs either had invariable accent on the root, or "mobile" accent which could alternate between root and ending in the inflectional paradigm.
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One direct consequence is that two apparently different exact solutions could correspond to the same model universe, and differ only in their coordinates. Ehlers began to look for serviceable ways of characterizing exact solutions invariantly, that is, in ways that do not depend on coordinate choice. In order to do so, he examined ways of describing the intrinsic geometric properties of the known exact solutions.B. Schmidt, Preface to During the 1960s, following up on his doctoral thesis, Ehlers published a series of papers, all but one in collaboration with colleagues from the Hamburg group, which later became known as the "Hamburg Bible".
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To complete a painting he works on it for months on end. His themes are romantic and mystical sometimes bizarre but his style remains invariantly realistic. One of his most memorable motifs is the recurring hedonistic centaur. “Sommertag” picture link (2007–09) is the present high point of his art. It captivates the observer via Kissing's characteristic objectivity, its large format and its reference to Diego Velázquez “The Triumph of Bacchus” Günter Meißner, Erich Kissing. 51°20’N12°23’E oder: Das Wunderbare in der Wirklichkeit, Kalender der Dresdner Bank 1993, Brönner Verlag Frankfurt/Main 1993 (“Los Borrachos”, 1628–29).
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In the case of a speech signal, inputs are spectral coefficients over time. In order to learn critical acoustic-phonetic features (for example formant transitions, bursts, frication, etc.) without first requiring precise localization, the TDNN is trained time-shift-invariantly. Time-shift invariance is achieved through weight sharing across time during training: Time shifted copies of the TDNN are made over the input range (from left to right in Fig.1). Backpropagation is then performed from an overall classification target vector (see TDNN diagram, three phoneme class targets (/b/, /d/, /g/) are shown in the output layer), resulting in gradients that will generally vary for each of the time-shifted network copies.
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In contemporary military and naval parlance the term gun has a very specific meaning and refers solely to any large-calibre, direct-fire, high-velocity, flat-trajectory artillery piece employing an explosive-filled hollowed metal shell or solid bolt as its primary projectile. This later usage contrasts with large-calibre, high-angle, low-velocity, indirect-fire weapons such as howitzers, mortars, and grenade launchers which invariantly employ explosive-filled shells. In other military use, the term "gun" refers primarily to direct fire weapons that capitalize on their muzzle velocity for penetration or range. In modern parlance, these weapons are breech-loaded and built primarily for long range fire with a low or almost flat ballistic arc.
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Theories grounded in the belief that different types of moral thinking appears in a sequence, from one way of thinking to another, invariantly, are considered stage theories. Both Kohlberg and Piaget's theories about the development of moral reasoning argue that development occurs in stages and that less complex reasoning strategies from lower stages are abandoned in favor of the more complex strategies from the next. In essence, a preference for higher levels of moral thinking is the underlying proposition of stage theories, although what makes higher level moral thinking superior to lower level moral thinking is unclear. However, stage theories tend to downplay the effect of social learning on the individual and the influence the environment can have in certain situations of moral reasoning.
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The concept of a tensor field can be generalized by considering objects that transform differently. An object that transforms as an ordinary tensor field under coordinate transformations, except that it is also multiplied by the determinant of the Jacobian of the inverse coordinate transformation to the wth power, is called a tensor density with weight w. Invariantly, in the language of multilinear algebra, one can think of tensor densities as multilinear maps taking their values in a density bundle such as the (1-dimensional) space of n-forms (where n is the dimension of the space), as opposed to taking their values in just R. Higher "weights" then just correspond to taking additional tensor products with this space in the range. A special case are the scalar densities.
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It is defined by the tendency for immune, affective, and behavioral defenses to be hypersensitive and overreactive, rather than insensitive or weakly expressed. Randolph Nesse maintains that this is a consequence of a typical payoff structure in signal detection: In a system that is invariantly structured with a relatively low cost of false positives and high cost of false negatives, naturally selected defenses are expected to err on the side of hyperactivity in response to potential threat cues. This general idea has been applied to hypotheses about the apparent tendency for humans to apply agency to non-agents based on uncertain or agent- like cues. In particular, some claim that it is adaptive for potential prey to assume agency by default if it is even slightly suspected, because potential predator threats typically involve cheap false positives and lethal false negatives.
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The Poynting vector occurs in Poynting's theorem only through its divergence , that is, it is only required that the surface integral of the Poynting vector around a closed surface describe the net flow of electromagnetic energy into or out of the enclosed volume. This means that adding a solenoidal vector field (one with zero divergence) to S will result in another field which satisfies this required property of a Poynting vector field according to Poynting's theorem. Since the divergence of any curl is zero, one can add the curl of any vector field to the Poynting vector and the resulting vector field S' will still satisfy Poynting's theorem. However the theory of special relativity, in which energy and momentum are defined locally and invariantly via the stress–energy tensor, shows that the above-given expression for the Poynting vector is unique.
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Several linguistic issues have arisen in relation to the spelling of the words euro and cent in the many languages of the member states of the European Union, as well as in relation to grammar and the formation of plurals. In official documents, the name "euro" must be used for the nominative singular in all languages, though different alphabets are taken into account and plural forms and declensions are accepted. In documents other than EU legal texts, including national legislation, other spellings are accepted according to the various grammatical rules of the respective language. For European Union legislation, the spelling of the words for the currency is prescribed for each language; in the English-language version of European Union legislation the forms "euro" and "cent" are used invariantly in the singular and plural, even though this departs from usual English practice for currencies.
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A linear fractional transformation defined by a matrix from PSL(2,C) will preserve the Riemann sphere P1(C) = C ∪ ∞, but will send the upper-half plane H to some open disk Δ. Conjugating by such a transformation will send a discrete subgroup of PSL(2,R) to a discrete subgroup of PSL(2,C) preserving Δ. This motivates the following definition of a Fuchsian group. Let Γ ⊂ PSL(2,C) act invariantly on a proper, open disk Δ ⊂ C ∪ ∞, that is, Γ(Δ) = Δ. Then Γ is Fuchsian if and only if any of the following three equivalent properties hold: # Γ is a discrete group (with respect to the standard topology on PSL(2,C)). # Γ acts properly discontinuously at each point z ∈ Δ. # The set Δ is a subset of the region of discontinuity Ω(Γ) of Γ. That is, any one of these three can serve as a definition of a Fuchsian group, the others following as theorems. The notion of an invariant proper subset Δ is important; the so-called Picard group PSL(2,Z[i]) is discrete but does not preserve any disk in the Riemann sphere.
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